Define reinforced concrete.
Reinforced cement concrete is a composite material is made of concrete and steel reinforcement. The concrete may be assumed to work purely in compression whereas the reinforcement is predominately subjected to tension. For a large range of applications it is sufficient to consider the uni-axial response of either material.
What is the purpose of using reinforced cement concrete?
Γ Plain cement concrete has very low tensile strength. The tensile strength of concrete is about one-tenth of its compressive strength. As a result, a plain concrete beam fails suddenly as soon as the tension cracks start to develop.
Γ To improve the tensile strength of concrete, some sort of reinforcement is needed which can take up the tensile stress developed in the structure.
Γ Itβs not only increases the strength but also in preventing the temperature and shrinkage.
Γ Therefore, reinforcing steel is added in the tension zone to carry all the developed tensile stresses.
What are the advantages of RCC when compared with other building materials?
Γ Concrete is workable when fresh and strong when hardens.
Γ It can be molded into any required shape and size.
Γ The raw materials required are easily available.
Γ Skill is not required for casting concrete elements.
Γ Concrete is durable, fire resisting and rigid.
Γ Concrete requires less maintenance.
What are the disadvantages of RCC when compared with other building materials?
Γ The self-weight of the structural elements will be more while concrete is used.
Γ Concrete has a very low tensile strength. Hence cracks will form in the tension zone if reinforcement is not provided properly.
Γ Cracks develop in concrete, also due to shrinkage, creep, temperature, etc. which permit seepage of water into the concrete. This causes corrosion of steel reinforcement and thereby peeling of concrete.
Γ Concrete has poor insulating property.
Γ Dismantling and reusing of concrete elements are mostly not possible.
Γ Concrete is brittle in nature and hence has low impact resisting capacity.
What are the uses of reinforced concrete?
It is used for the construction of,
Γ Buildings
Γ Bunkers and silos
Γ Chimneys and towers
Γ Flyovers
Γ Retaining walls
Γ Roads and railway bridges
Γ Water tanks
What are the types of load on R.C.C structures?
Γ Dead load
Γ Live load or Imposed load
Γ Wind load
Γ Snow load
Γ Earthquake load
Γ Seismic load
What are the elements of structures?
Γ Beam
Γ Column
Γ Floor
Γ Foundation
Γ Slab
Γ Staircase
What are the methods of design?
Γ Modular Ratio Method (or) Working Stress Method(WSM) (or) Elastic Method of Design
Γ Load Factor Method (or) Ultimate Load Method(ULM) (or) Ultimate Strength Method
Γ Limit State Method(LSM)
Define elastic method of design.
The elastic method of design of reinforced concrete member is also known as Working Stress Method (or) Modular Ratio Method. Elastic behaviors of materials are used in Elastic Method of Design. The method of elastic design of a structure is defined as a method which limits the structural usefulness of the material of the structure upto a certain load at which the maximum stress in extreme fibre reaches the characteristic strength of material in bending.
Define ultimate load design method.
This method is otherwise known as Load Factor Method or Ultimate Strength Method. This method is based on the ultimate strength, when the design member would fail. In this method factors are taken into account only on loads are load factors. The method of ultimate design of a structure is defined as a method which limits the structural usefulness of the material of the structure upto ultimate load.
Define limit state method.
The Limit State Method is defined as a method which limits the structural usefulness of the material of the structure upto a certain load at which acceptable limit of safety and serviceability are applied so that the failure of structure does not occur. It is the combination of Working Stress Method and Ultimate Load Method. In this method partial factor of safety is considered on both loads and stresses. This method is advance over other methods. Since, safety and serviceability are considered.
Define characteristic load.
A characteristic load is defined as that value of load which has a 95% probability of not being exceeded during the life of the structure.
πΉπ= πΉπ+ πΎ ππ
Where,
Fk = characteristic load
Fm = mean load
K = constant = 2.645 β 2.65
Sd = standard deviation for the load
Define permissible stress.
It is defined as the ratio of yield stress to the factor of safety. ππππππ π ππππ π π‘πππ π = πππ‘ππππ‘π ππ πππππ π π‘πππππ‘β ππ πππ‘ππππππ πΉπππ‘ππ ππ πππππ‘π¦
Define factor of safety.
Factor of safety is a number used to determine the working stress. It is fixed based on the experimental works on the material. It accounts all uncertainties such as, material defects, unforeseen loads, manufacturing defects, unskilled workmanship, temperature effects etc. Factor of safety is a dimensionless number. It is defined as the ratio of ultimate stress to working stress for brittle materials or yield stress to working stress for ductile material.
πΉππ= πππ‘ππππ‘π π π‘πππ π πππππππ π π‘πππ π (πππ ππππ‘π‘ππ πππ‘πππππ)
Define modular ratio.
It is defined as the ratio of elastic modulus of steel to that of concrete. It is used to transform the composite section into an equivalent concrete section. π= 2803 ππππ
What is the expression recommended by the IS 456-2000 for modulus of elasticity?
ππππ’ππ’π ππ ππππ π‘ππππ‘π¦= πΈπ=5000 βπππ
State the assumption made for design of RC members in working stress method.
(Refer IS 456:2000 Page no: 80)
What are the advantages in limit state method?
Γ Ultimate load method only deals with on safety such as strength, overturning, and sliding, buckling, fatigue.
Γ Working stress method only deals with serviceability such as crack, vibration, deflection etc.
Γ But, Limit state method advances than other two methods. Hence by considering safety at ultimate load and serviceability at working load.
Γ The process of stress redistribution and moment redistribution are considered in the analysis and more realistic factor of safety values are used in the design. Hence, the design by limit state method is found to be more economical.
Γ The overall sizes of flexural members arrived by limit state method are less and hence they provide better appearance to the structure.
What are the advantages of working stress method?
Γ The design usually results in relatively large sections of structural members, compared to ultimate load. Due to this structures designed by working stress method gives better serviceability performance under working loads.
Γ This method is only the method available when one has to investigate the reinforced concrete section for service stresses and for the serviceability state of deflection and cracking.
What are the disadvantages of working stress method?
Γ The WSM does not show the real strength nor gives the true factor of safety of the structure under failure.
Γ The modular ratio design results in larger percentage of compression steel than that given by the limit state design, thus leading to un-economic design.
Γ Because of creep and non-linear stress-strain relationship, concrete does not have definite modulus of elasticity.
Γ The WSM fails to discriminate between different types of loads that act simultaneously but have different uncertainties.
What are the advantages of ultimate load method?
Γ While the WSM uses only the nearly linear part of stress-strain curve, the ULM uses fully the actual stress-strain curve.
Γ The load factor gives the exact margin of safety against collapse.
Γ The method allows using different load factors for different types of loads and the combination thereof.
Γ The failure load computed by ULM matches with the experimental results.
Γ The method is based on the ultimate strain as the failure criteria.
Γ The method utilizes the reserve of strength in the plastic region.
What are the disadvantages of ultimate load method?
Γ The method does not take into consideration the serviceability criteria of deflection and cracking.
Γ The use of high strength reinforcing steel and concrete results in increase of deflection and crack width.
Γ The method does not take into consideration the effects of creep and shrinkage.
Γ In the ULM, the distribution of stress resultants at ultimate load is taken as the distribution at service loads magnified by the load factor. This is erroneous since significant redistribution of stress resultants takes place as the loading is increased from service loads to ultimate loads.
What are the factors considered in limit state of collapse?
Γ Flexure
Γ Compression
Γ Shear
Γ Torsion
What are the factors considered in limit state of serviceability?
Γ Cracking
Γ Deflection
Γ Durability
Γ Fire resistance
Γ Vibration
What are the factors of safety in limit state?
Γ Partial factor of safety for concrete πΎπ=1.5
Γ Partial factor of safety for steel πΎπ =1.15
Γ Partial factor of safety for load πΎπ
Write down the value of partial safety factor for concrete and steel.
Γ Partial factor of safety for concrete πΎπ=1.5
Γ Partial factor of safety for steel πΎπ =1.15
What is under reinforced section?
Steel reaches maximum permissible stress earlier than concrete due to external loads is called under reinforced section.
What is over reinforced section?
Concrete reaches maximum permissible stress earlier than steel due to external load is called over reinforced section.
What is balanced section?
Concrete and steel reaches maximum permissible stress simultaneously due to external load is called balanced section.
Define singly reinforced section.
Steel reinforcements are provided only on tension zone of RC flexural member is known as singly reinforced section.
Define doubly reinforced section.
Steel reinforcements are provided on both tension and compression zone of RC flexural member is known as doubly reinforced section.
In some situations it becomes essential for a beam to carry BM more that it can resist as a balanced section. In this case additional reinforcement is provided in compression zone such beams reinforced in both compression and tension zones are known as doubly reinforced section.
Under what circumstances doubly reinforced beams resorted to?
When,
ππ’> ππ’ πππππ‘. Then, doubly reinforcement is used.
Write down the basic values of span to effective depth ratio for the different types of beam.
Basic values of span to effective depth ratios for spans up to 10m
Cantilever
7
Simply supported
20
Continuous
26
Define collapse state.
The limit state of collapse of the structure or part of the structure could be assessed from replace of one or more critical sections and from bulking due to elastic or plastic instability or overturning.
Define the terms Gross section, Transformed section, cracked section.
(Refer IS 456:2000 Page no: 35)
Draw the stress-strain curve for concrete, mild steel bars and HYSD bars.
Define brittle and ductile failure.
Materials that fracture without any plastic deformation are called brittle materials. Example: Glass and other ceramic materials.
Materials undergo plastic deformation before fracture is called ductile material. Example: aluminum, copper, steel and many metals, as well as polyethylene, nylon and many other polymers.
Define clear cover.
The distance between the bottom of the bars and bottom most edge of the beam is called clear cover.
Define effective cover.
The distance between the centre of the reinforcement bar and the bottom edge of the beam is called effective cover. πΈπππππ‘ππ£π πππ£ππ = πππππ πππ£ππ + ππππππ‘ππ ππ πππ2
UNIT β 2
What do you understand by development length of bar?
The reinforced bar must extend in the anchorage zone of concrete sufficiently, to develop the required stress. The extended length of bar inside the face of the support is known as development length. It is denoted by the symbol, Ld.
Define anchorage length.
Anchorage length is defined as embedded portion of the bar in concrete, but not subjected to any flexural bond.
Define anchorage bond.
All the types of reinforcement must be anchored within the concrete section, in order that the anchorage bond should be sufficient to develop the stress in the bar. The anchorage depends on the bond between the bar and concrete and the area of contact.
Define curtailment of bars.
In flexural members, design of reinforcement is done based on bending moment along the span. As the magnitude of bending moment on a beam decreases along its length, that case the area of bending reinforcement may be reduced by curtailing bars as they are no longer required.
What do you mean by equilibrium torsion?
Torsion induced by eccentric loading and equilibrium condition alone sufficient to determine twisting moments is known as equilibrium torsion.
Define torsion.
Equal and opposite moments applied at both ends of structural element or its part about its longitudinal axis is called torsion. It is also called as torsional moment or twist or torque.
What is compatibility torsion?
Torsion induced by application of an angle of twist and the resulting moment depends on the torsional stiffness of the member is known as compatibility torsion.
How can torsional resistance of RC members be enhanced?
Increasing strength of concrete and the amount of longitudinal as well as transverse reinforcements over and above those required for bending and shear can enhance the torsional resistance of a member.
Name the locations in beam where the development lengths of torsion bars should be checked.
At beams, development lengths should be checked at the sections where,
Γ Maximum bending moment occurs
Γ Point of curtailment
Γ Point of inflation
Write down the effect of torsion in RC beams.
RC members may be subjected to torsion in combination with bending and shear. Longitudinal and transverse reinforcement shall be provided for RC beams to resist torsion.
Torsional reinforcement is not calculated separately from that required for bending and shear. Instead, the total longitudinal reinforcement is determined for a fictitious bending moment which is a function of actual bending moment and torsion.
Write about local bond and anchorage length.
All types of reinforcement must be anchored within the concrete section, in order that the anchorage bond should be sufficient to develop the stress in the bar. Anchorage length is defined as embedded portion of the bar in concrete, but not subjected to any flexural bond.
Distinguish between flexural bond and development bond.
FLEXURAL BOND
DEVELOPMENT BOND
It arises in flexural members on account of shear or variations in bending moment, which in turn causes a variation in axial tension along the length of a reinforcing.
It arises over the length of anchorage provide for a bar or near the end of a reinforcing bar.
Why is bond stress more in compression bars than in tension bars?
Γ Deformed bars subjected to tension, πππ values shall be increased by 60%.
Γ Deformed bars subjected to compression, πππ values shall be increased by 25%.
What are the types of reinforcement used to resist shear and write down the expressions for to shear resistance offered by the type?
Shear reinforcement is necessary if the nominal shear stress (ππ£) exceeds the design shear stress(ππ). In general, shear reinforcement is provided in any one of the following three forms. (Refer IS 456:2000 Page no: 72)
Write down the value of design bond stress for M30 grade of concrete.
Design bond stress in limit state methods for plain bars (mild steel) in tension is πππ=1.5 πππ2
What is RC slab?
Reinforced concrete slabs are used in roofs of buildings. Slab is a flexural member transmits imposed and dead load to the supports. Support may be a wall, beam or column.
Reinforced concrete slabs are generally safe and do not require shear reinforcement. Why?
Normally the thickness of slab is so chosen that the shear can be resisted by concrete itself and the slab does not need extra shear reinforcements.
What are the types of slab?
Γ One way slab
Γ Two way slab
How can be classified the slab?
Γ πΏπ¦πΏπ₯>2 (One way slab)
Γ πΏπ¦πΏπ₯<2 (Two way slab)
Define one way slab.
When the slab is supported only on two opposite sides, the slab bends in one direction only. Hence, it is called one way slab.
Define two way slabs.
When the slab is supported on all four sides, the slab bends in both directions. Hence, it is called two way slabs.
Name the two types of two-way slabs. Explain their difference in the design of slabs.
Γ Slabs simply supported on the four edges, with corners not held down and carrying UDL
Γ Slabs simply supported on the four edges, with corners held down and carrying UDL
Γ Slabs with edges fixed or continuous and carrying UDL
Why is secondary reinforcement provided in one way RC slab?
Secondary reinforcement is provided running perpendicular to the main reinforcement, in order to take the temperature and shrinkage stresses. It is otherwise called as distribution or temperature reinforcement.
What are the codal provisions for a minimum reinforcement to be provided as main and secondary reinforcement in slab and their maximum spacing?
Minimum reinforcement:
π΄π π‘= 0.15100 Γπ Γπ· (For mild steel)
(π΄π π‘)πππ = 0.15100 Γπ Γπ· (For HYSD bars)
Γ Spacing = 3d or 300mm (horizontal distance between parallel main reinforcement bars). Use whichever is smaller.
Γ Spacing = 5d or 450mm (horizontal distance between parallel reinforcement bar provided against shrinkage and temperature). Use whichever is smaller.
Explain the purposes of lintel beams in buildings.
Lintels are provided over the openings of doors, windows, etc. Generally, they support the load of the wall over it, and sometimes also the live loads are transferred by the sub-roof of the room. Lintel takes the masonry load over the openings and distributes to the masonry located sides of opening.
What type of slab usually used in practice, under reinforced or over reinforced section?
The depth of slab chosen from deflection requirements will be usually greater than the depth required for balanced design. Hence the area of steel required will be less than the balanced amount. So, the slab is designed as under reinforced section.
What do you understand by flanged beam?
The concrete in the slabs, which is on the compression side of the beam, can be made to resist the compression forces, and the steel in the tension side of the beam can carry the tension. These combined beam and slab units are called flanged beam.
Define shear strength.
The resistance to sliding offered by the material of beam is called shear strength.
What are the important factors affecting the shear resistance of a reinforced concrete member without shear reinforcement?
Γ Characteristic strength of concrete
Γ Percentage of longitudinal steel
Γ Shear span to depth ratio
Γ Axial compressive/tensile force
Γ Effect of cross section
Γ Effect of two way action
UNIT β 3
Define column.
A column, in general, may be defined as a member carrying direct axial load which causes compressive stresses of such magnitude that these stresses largely control its design.
Γ It transmits load coming from beam or slab and distributes to the foundation usually columns are square, rectangle, circular and βIβ shaped in cross section.
Γ It is reinforced with longitudinal and lateral ties.
Γ Load carrying capacity of column is depending upon longitudinal steel and cross sectional size of the column.
Γ Lateral ties are giving lateral support to the longitudinal steel. The columns are analyzed for axial force and moments.
Differentiate between long and short column.
Based on slenderness ratio (Ξ») columns can be classified into long and short.
Slenderness ratio (Ξ») = πΈπππππ‘ππ£π πππππ‘βπΏπππ π‘ πππ‘ππππ ππππππ πππ
Short column Ξ» < 12 Long column Ξ» > 12
Differentiate between uni-axial and bi-axial bending.
Axial load and bending moment along one direction are applied simultaneously on the column is called uni-axial bending.
Axial load and bending moment along two direction are applied simultaneously on the column is called bi-axial bending.
According to IS code all columns should be designed for minimum eccentricity. Justify the statement.
Lateral loads such as wind and seismic loads are not considered in design.
Γ Misalignment in construction
Γ Slenderness effects not considered in design
Γ Accidental lateral or eccentric loads
Write down the formula for calculating minimum eccentricity.
ππππ= π500+ π·30 , subject to a minimum of 20mm
Where,
l = unsupported length of the column
D = lateral dimension of the column
What is spiral column?
For a circular column, longitudinal tied with closely spaced helix are called as spiral column.
What is the minimum and maximum percentage of reinforcement can be provided for a column?
The cross sectional area of longitudinal reinforcement shall be not less than 0.8% not more than 6% of the gross cross sectional area of the column.
What are the specifications for pitch of lateral ties in columns?
The pitch of the transverse reinforcement shall be not more than the least of the following distances:
Γ Least lateral dimension of the compression member
Γ Sixteen times the smallest diameter of the longitudinal reinforcement bar to be tied.
Γ 300mm
What is pedestal?
Pedestal is a compression member, the effective length of which does not exceed three times the least lateral dimension.
Distinguish braced and un-braced column.
BRACED COLUMN
UNBRACED COLUMN
In most of the cases, columns are subjected to horizontal loads like wind, earthquake, etc. If lateral supports are provided at the ends of the column, the lateral loads are borne entirely by the lateral supports. Such columns are known as braced columns.
Other columns, where the lateral loads have to be resisted by them, in addition to axial loads and end moments, are considered as un-braced columns.
It is not subject to side sway.
It is subject to side sway.
What is slender column?
If the slenderness ratio of the column about either axis is greater than 12, is classified as long column. Long column should be designed as slender column.
Mention the functions of the traverse reinforcement in a RC column.
Γ To prevent longitudinal buckling of longitudinal reinforcement.
Γ To resist diagonal tension caused due to transverse shear due to moment / transverse load.
Γ To hold the longitudinal reinforcement in position at the time of concreting.
Γ To confine the concrete, thereby preventing its longitudinal splitting.
Γ To impart ductility to the column.
Γ To prevent sudden brittle failure of the column.
Classify the column according to the material.
Γ Pre-stressed concrete
Γ Reinforced cement concrete
Γ Stone
Γ Timber
Classify the column according to transverse reinforcement.
Γ Spiral or helical
Γ Tied
UNIT β 4
What are the types of foundations?
Γ Deep foundation
Γ Shallow foundation
What are the types of shallow foundations?
Γ Combined footing
Γ Isolated footing
Γ Mat or raft footing
Γ Spread or strip footing
Γ Strap or cantilever footing
What are the types of deep foundations?
Γ Pier foundation
Γ Pile foundation
Γ Well foundation
What are the factors governing to decide the depth of footing?
The footing is generally to resist the bending moments and shear forces developed due to soil reactions. The main purpose of the footing is to effectively support the super structures.
Define safe bearing capacity of soil.
It is the maximum intensity of load or pressure developed under the foundation without causing failure of soil. Unit for safe bearing capacity of soil isπππ2. Safe bearing capacity of soil is determined by the plate load test at the site.
What is punching or two way shear in RCC footing?
Punching shear is a type of shear failure occurs in reinforced concrete footings due to axial load from the column and upward soil thrust from the ground.
What are the advantages of providing pedestals to columns?
Γ Where pedestals are providing, and full force is transferred to the footing without additional reinforcement.
Γ Pedestal provides a plane surface for the convenience of column construction.
What is the situation in which trapezoidal shape is preferred to a rectangular shape for a two column combined footing?
If the one column is carrying load is much larger than the other one, trapezoidal combined footing is preferred.
When combined footings are adopted?
Γ When two or more columns/walls are located close to each other and/or if they are relatively heavily loaded and/or rest on soil with low safe bearing capacity.
Γ An exterior column located along the periphery of the building is so close to the property line that an isolated footing cannot be symmetrically placed without extending beyond the property line.
Under what circumstances rectangular shape preferred for a two-column combined footing.
When loads are equal and no restriction on sides, the footing will be rectangular with equal overhang on both sides.
Under what circumstances combined footing is preferred.
Γ When isolated footings for individual columns are touching or overlapping each other.
Γ When the columns are located near the boundary lines or expansion joints.
What is meant by eccentric loading on a footing and under what situation does this occur?
The load P acting on a footing may act eccentrically with respect to the centroid of the footing base. This eccentricity may result from one or more of the following effects.
Γ The column transmitting a moment M in addition to the vertical load.
Γ The column carrying a vertical load offset with respect to the centroid of the footing.
Γ The column or pedestal transmitting a lateral force located above the foundation level, in addition to the vertical load.
Write down the formula for calculating maximum and minimum soil pressures for a rectangular footing carries eccentric point load.
The structural design of the footing, which includes the design of the depth and reinforcement, is done for factored loads using the relevant safety factors applications for the limit state of collapse.
Define stair case.
Staircase flights are generally designed as slabs spanning between wall supports or landing beams or as cantilever from a longitudinal inclined beam. The staircase fulfills the function of access between the various floors in the building. Generally the flight steps consist of one or more landings between the floor levels.
What are the components of stairs?
The components of stairs are,
Γ Baluster
Γ Flight
Γ Going
Γ Landing
Γ Rise
Γ Riser
Γ Soffit
Γ Step
Γ Tread
Γ Winders
What are the normal range of tread and rise values of steps of a staircase in residential building?
As per IS 456:2000 the normal range of tread and rise values of steps of a staircase in residential building are,
Γ Rise: 150mm to 180mm
Γ Tread: 200mm to 250mm
List the various types of stair cases.
Γ Bifurcated stairs
Γ Dog-legged stairs
Γ Geometrical stairs such as circular, spiral stair, etc
Γ Multi-flight stairs
Γ Open newel stair with quarter space landing
Γ Quarter-turn stairs
Γ Straight stairs
Γ Three quarter-turn stairs
Define flat slab.
A flat slab is a reinforced concrete slab supported directly over columns without beams generally used when headroom is limited such as in cellars and warehouses.
Define Box Culvert.
These are provided for conveying water to serve the following requirements:
Γ To serve as means for a cross drainage
Γ To provide a supporting slab for road way under which the cross drainage flows
What are cases available in Box Culvert?
Γ Case (I) when the top slab carries the dead and live load and culvert is empty
Γ Case (II) when the top slab carries the dead and live load and culvert is full of water
Γ Case (III) when the sides of culvert do not carry live load and culvert is full of water.
How the effectively span of a stair is decided when the landing slab spans in the same direction as the stair.
When the landing slab spans in the same direction as the stairs, they should be considered as acting together to form a single slab and the span determined at the distance centre to centre of the supporting beams or walls, the going being measured horizontally.
Give the guidelines of the size of rise and tread as per IS code norms.
The following guidelines may be followed while deciding the size of rise and tread of a stair.
Γ 400mm < (rise + tread) < 450mm
Γ 580mm < (rise + tread) < 630mm
Define depth of section.
The depth of section shall be taken as the minimum thickness perpendicular to the soffit of the staircase.
How the load is distributed in the case of an open well stairs?
In the case of stairs with open wells, where spans partly crossings at right angles occur, the load on areas common to any two such spans may be taken as one-half in each direction.
How the load is distributed when flights or landings are embedded into walls?
Where flights or landings are embedded into walls for a length not less than 110 mm and designed to span in the direction of the flight, a 150 mm strip may be deducted from the loaded area and effective breadth of the section increased to 75 mm for the purpose of design.
What are the loads acting on staircases? Explain.
DEAD LOADS:
Self-weight of stair slab which includes the waist slab, tread-rise, etc. Self-weight of finishes (0.5 to 1 kN/m2)
LIVE LOADS:
IS 875 parts II specifies the load to be considered as UDL of intensity 5kN/m2 for public buildings and 3kN/m2 for residential building where the specified floor do not exceed 2kN/m2 and the staircases are should not liable for overcrowding.
Explain structural behaviors of stair cases.
Staircases can be grouped depending upon the support conditions and the direction of major bending of the slab component under the following categories.
Γ Staircase slab spanning horizontally (along the slope line)
Γ Staircase slab spanning transversely (slab width wise with central or side supports)
UNIT β 5
What is masonry?
Masonry is a structure built of in individual blocks of materials such as stone, brick, concrete, hollow blocks, etc bonded together with some form of mortar such as lime mortar, cement mortar.
What is the size of bricks?
Without mortar joints:
Γ Size of standard brick = 190mm x 90mm x 90mm
Γ Size of modular type brick = 190mm x 90mm x 40mm
With mortar joints:
Γ Size of brick = 200mm x 100mm x 100mm
Γ Size of modular type brick = 200mm x 100mm x 50mm
List the Types of bricks.
Γ Common clay bricks
Β· Class I bricks
Β· Class II bricks
Β· Class III bricks
Γ Heavy duty bricks
Β· Class I bricks (or) A class bricks
Β· Class II bricks (or) B class bricks
Define Mortar.
Mortar is a combined material formed with intimately mixing a binding material like lime or cement, with a fine aggregate like sand in certain proportion and with adequate quantity of water.
What is the classification of Walls?
Γ Load bearing walls
Β· Cavity wall
Β· Faced wall
Β· Solid wall
Β· Solid wall with piers (pilaster)
Β· Veneered wall
Γ Non-load bearing walls
Β· Curtain wall
Β· Free-standing wall
Β· Panel wall
Β· Partition wall
What are the classifications of loads on walls?
Γ Axial (or) Vertical
Γ Lateral (or) transverse
Define criteria.
Design criterion is that the actual stress produced due to loads in the structure should be within permissible limits.
What are the factors of permissible stress (or) allowable compressive stress?
Γ Cross sectional area of the masonry
Γ Eccentricity of loading
Γ Shape and size of bricks
Γ Slenderness ratio
Γ Strength of mortar
Γ Type and strength of bricks
What is the purpose of providing a lateral support into a masonry structure?
Masonry structures gain stability from support offered by cross walls, floors and roofs. Lateral supports for load bearing walls or columns limit the slenderness of the structure. Further the lateral support reduces the possibility of buckling of member due to vertical loads and to resist horizontal forces.
What is a pilaster in bricks masonry wall?
Solid walls are thickened at intervals by increasing the cross section. The thickened portions are called as piers or pilasters. They are used for one of the following purposes.
Γ To carry concentrated loads from roof or floor beams
Γ To provide lateral support
Γ To reduce the slenderness ratio by stiffening the walls.
What is meant by slenderness ratio of a masonry wall?
ππππππππππ π πππ‘ππ= ππππππ‘ππ£π βπππβπ‘ ππππππ‘ππ£π π‘βππππππ π
What is an equivalent eccentricity?
In an eccentricity loaded wall, there is an axial load and a bending moment these two may be combined into single resultant load acting at a distance. This is known as equivalent eccentricity.
List the factors which contribute for eccentricity on bricks walls.
Γ Geometry of the support
Γ Long floor edges
Γ Magnitude of loads
Γ Relative stiffness of slab or beam and the wall
Γ Unequal spans
How do you determine the average effective thickness of wall with opening?
π΄πππ (π΄) = (πΏβπ) Γ π‘ πΈπππππ‘ππ£π π‘βππππππ π (π‘)= (πΏβπ)
Where,
L = length between outer wall faces
a = width of spacing
t = thickness of wall
Define Retaining walls.
Retaining walls are structures used to provide stability of earth masses other loose materials. That is when field conditions do not allow the earth pressure to assume its natural shape or when abrupt changes in the ground surface elevation are needed retaining walls are used.
Where are used the retaining walls?
Γ Basement wall
Γ Box culvert
Γ Depressed roads
Γ Elevated protection
Γ Erosion protection
Γ Flood wall
Γ For underground water tanks
Γ Landscaping
Γ Retaining a rail-road or highway in hilly area
Γ Used at the ends of bridges in the form of abutments
Types of retaining walls.
Γ Buttressed wall:
A buttressed wall is a modification of the counter fort retaining wall in which the counterforts, called the buttresses, are provided to the other side of the backfill. However the buttresses reduce the clearance in front of the wall, and therefore these walls are not commonly used.
Γ Cantilever retaining wall:
A taller wall with extended toe and heel to offset the large lateral pressure tends to overturn the wall. A cantilever wall has part of the base extending underneath the backfill, and the weight of the soil above this part of the base helps prevent overturning.
Β· T-shaped
Β· L-shaped
Γ Counter fort retaining wall:
The vertical stem and the heel slab are strengthened by providing counterforts at some suitable intervals. Because of provision of counterforts, the vertical stem as well as the heel slab acts as continuous slab, in contrast to the cantilevers of cantilever retaining wall. The toe slab however acts as cantilever bending upwards. This type of retaining wall is used when backfill of greater height is to be retained.
Γ Gravity retaining wall:
A gravity retaining wall is the one which resists the lateral earth pressure by its weight in contrast to the cantilever and counter fort retaining walls in which the pressure is resisted by bending action. A gravity retaining wall is therefore, thicker in section. They are constructed of mass concrete, brick or stone masonry.
Β· Massive Gravity Wall
Β· Counter fort Wall
Β· Cantilever Gravity Wall
What are the assumptions for coulombβs earth pressure theory?
The earth pressure theory proposed by coulomb is based on the following assumptions:
Γ The soil or the retained material is isotropic, homogeneous and possesses both internal friction and cohesion.
Γ The rupture surface is a plane surface.
Γ The friction forces are uniformly distributed along the plane rupture surface.
Γ The failure used is a rigidly body.
Γ There is a wall friction.
Γ Failure is a Plane strain problem.
What is the structural action of the stem, heel and toe?
STEM:
The vertical arm or stem is subjected to lateral pressure and acts as a cantilever. The lateral pressure causes maximum bending moment and shear forces at junction of the stem.
HEEL:
The heel is subjected to soil pressure from the bottom acting towards and the downward loads due to self-weight and the earth above the heel. The downward load is more hence the heel acts like a cantilever is more hence the heel acts like a cantilever bending downwards. Maximum bending moment and shear force occur at the junction of the heel with stem.
TOE:
The toe is subjected to upward pressure from the soil and the downward pressure is due to self-weight. Hence the toe is designed as cantilever. Maximum bending moment and shear force occur at the face of the stem.
How the development of tension in a base slab is checked?
In order to avoid development of tension in the base slab, the resultant of various forces acting on the wall should cut the base in the middle-third of the width of the base. Further the maximum pressure on the base slab should not exceed the allowable soil pressure.
Why counter forts are provided in a counter fort retaining wall?
In a cantilever retaining wall with more height, the bending moment development in the stem, heel slab and toe slab become very large and require thickness. The bending very large and require moments and so the thickness. The bending moments and so the thickness of stem and slab can be considerably reduced by introducing transverse supports called counter forts. They are spaced at regular intervals of about 0.3 to 0.6hl where βhβ is the height of the retaining wall. The counter forts are concealed within the backfill.
What are the factors governing the spacing of counter forts?
Spacing of counter forts depends on various factors such as height of retaining wall, cost of steel and concrete, allowable soil pressure and cost of form work. Keeping the spacing of counter forts closer reduces the thickness of vertical slab and the heel slab and cost of formwork increases.
Thus the spacing is the one which makes the design economical. Spacing generally varies from n0.3 to 0.6h where βhβ is the height of the wall.
Define the stability of retaining wall structure.
Retaining wall as a wholes stability the following external stability requirements:
Γ Safety against bearing capacity failure
Γ Safety against overturning
Γ Safety against sliding
Define factor of safety against overturning.
Factor of safety against sliding along the base is defined as the ratio of resisting moment to disturbing moment about the toe. Factor of safety against sliding should not be less than 2.0
What do you mean by the backfill of retaining wall?
Loose material like soil, coal or ore piles retained on the back of a retaining wall is called a backfill. Backfill materials for retaining structure should be designed to minimize the lateral pressure. A good backfill material should satisfy two important requirements via, high long β term strength and free drainage. Granular materials make the best types of backfill.
List out the various forces subjected to a cantilever retaining wall.
The forces are,
Γ Wc = weight of the cantilever wall
Γ Wa = weight of soil above the back fill
Γ Pa = lateral pressure from backfill
Γ Pp = lateral pressure at the front of the wall
Γ Pmax & Pmin = soil pressures beneath the retaining wall
What is the function of a shear key?
A retaining wall should be safe against overturning, sliding and bearing capacity failure. The horizontal forces causing sliding forces are the steering resistance offered at the base and the passive resistance before the wall. A main FOS of 1.5 is generally provided. If adequate forces not achieved, a shear key is incorporated in the base.
Define Active and Passive Earth Pressure.
Active Earth Pressure:
It is the pressure that at all times are tending to move or overturn the retaining wall.
Passive Earth Pressure:
It is reactionary pressures that will react in the form of a resistance to movement of the wall.
What are the Effects of Active and Passive Earth Pressure?
Active Earth Pressure:
It is composed of the earth wedge being retained together with any hydrostatic pressure caused by the presence of groundwater. This pressure can be reduced by:
Γ The use of subsoil drainage behind the wall.
Γ Inserting drainage openings called weep holes through the thickness of the stem to enable the water to drain away.
Passive Earth Pressure:
It builds up in front of the toe to resist the movement of the wall if it tries to move forward. This pressure can be increased by enlarging the depth of the toe or by forming a rib on the underside of the base.
What are the factors to be considered while designing the Retaining Walls?
Γ Overturning doesnβt occur
Γ Sliding doesnβt occur
Γ The soil on which the wall rests mustnβt be overloaded
Γ The materials used in construction are not overstressed.
What are the forces or pressure that has to be calculated while designing the retaining walls?
Γ Height of water table
Γ Nature and type of soil
Γ Subsoil water movements
Γ Type of wall
Γ Material used in the construction of wall
What are the various loads considered in heel slab of Retaining Walls?
Γ Weight of the backing
Γ Dead load on heel slab
Γ Vertical component of lateral
Γ Upward soil reaction
What do you mean by surcharge angle?
The position of the backfill lying above the horizontal plane at the elevation of the top of a wall is called the surcharge, and its inclination to the horizontal is called the surcharge angle Ξ².
What is angle of internal friction (Ξ¦)?
The angle of internal friction which is equal to the ratio of the maximum resistance to sliding on any internal plane to the normal pressure acting on the plane
What are the points to be noted in the design of Cantilever Retaining Wall?
Γ The thickness of the stem may be kept the same throughout the height to provide adequate
Γ Dead load
Γ The base slab may be made about 100mm thicker than stem
Γ The width of the base slab may be kept about 0.7 to 0.8 times the total height of the wall
Γ It may most probably require a key to be provided to have a safe factor of safety against sliding
What are the loads acting on the heel slab of the Counter fort Retaining Wall?
Γ Dead load of the strip
Γ Weight of the earth above the strip
Γ Vertical components of the lateral pressure in the case of the earth surcharged at an angle.
What are the structural components of Retaining Walls?
Base, heel, toe, stem and backfill are the structural components of a retaining wall.
What are the components of counter fort retaining wall?
Upright slab:
Its design as a continuous slab spanning horizontally on the Counter fort subjected to lateral earth pressure
Base slab:
The width of the base slab may be taken as 0.6H to0.7H
Where,
H= overall height of the retaining wall.
Heel slab:
The Heel slab should be designed as a continuous horizontal slab with counter fort as the supports.
State the advantages of pre-stressed concrete over reinforced concrete.
Γ Since the technique of pre-stressing eliminates cracking of concrete under all stage of loading, the entire section of the structures takes part in resisting the external load. In contrast to this, in the reinforced concrete, only portion of concrete above the neutral axis is effective.
Γ Since concrete does not cracks, the possibility of steel to rust and concrete to deteriorate is minimized.
Γ Absence of cracks results in higher capacity of the structure to bear reversal of stresses, impact, vibration and shock.
Γ In pre-stressed concrete beams, dead loads are practically neutralized. The reactions required are therefore, much smaller than required in reinforced concrete. The reduced dead weight of structure results in saving in the cost of foundations. The neutralization of dead weight is of importance in large bridges.
Γ The use of curved tendons and the pre-composition of concrete help to resist shear.
Γ The quantity of steel required for pre-stressing about 1/3 of that required for reinforced concrete, though the steel for the former should have high tensile strength.
Γ Pre-stressed concrete beams have usually low deflection.
Γ In pre-stressed concrete, precast blocks and elements can be assumed and used as one unit. This saves in the cost of shuttering and centring for large structures.
STRUCTURAL ANALYSIS β 1
UNIT β 1
Name any two force methods to analyze the statically indeterminate structures.
Γ Column analogy method
Γ Flexibility matrix method
Γ Method of consistent deformation
Γ Theorem of least work
Write the general steps of the consistent deformation method.
Γ By removing the restraint in the direction of redundant forces, released structure (which is a determinate structure) is obtained.
Γ In this released structure, displacements are obtained in the direction of the redundant forces.
Γ Then the displacement due to each redundant force is obtained and the conditions of displacement compatibility are imposed to get additional equations.
Γ Solution for these equations gives the values of redundant forces.
Γ Then the released structure subjected to these known forces gives the forces and moments in the structure.
Give example of beams of one degree static indeterminacy.
In general, πΈ=πβπ
For this case, π=4 πππ π=3
β΄ πΈ= 4 β 3 = 1
Define degree of kinematic indeterminacy (or) Degree Of Freedom.
It is defined as the least no of independent displacements required to define the deformed shape of a structure. There are two types of DOF
Γ Joint type DOF
Γ Nodal type DOF
Differentiate external redundancy and internal redundancy.
In pin jointed frames, redundancy caused by too many members is called internal redundancy. Then there is external redundancy caused by too many supports. When we introduce additional supports/members, we generally ensure more safety and more work (in analysis).
Why to provide redundant members?
Γ To maintain alignment of two members during construction
Γ To increase stability during construction
Γ To maintain stability during loading (Ex: to prevent buckling of compression members)
Γ To provide support if the applied loading is changed
Γ To act as backup members in case some members fail or require strengthening
Γ Analysis is difficult but possible
What are the different methods used to analyze indeterminate structures?
Γ Finite element method
Γ Flexibility matrix method
Γ Stiffness matrix method
What are statically indeterminate structures? Give example.
If the conditions of statics i.e., Ξ£H=0, Ξ£V=0 and Ξ£M=0 alone are not sufficient to find either external reactions or internal forces in a structure, the structure is called a statically indeterminate structure.
Define consistent deformation method.
This method is used for the analysis of indeterminate structure. This method is suitable when the number of unknown is one or two. When the number of unknown becomes more, it is a lengthy method.
Define primary structure.
A structure formed by the removing the excess or redundant restraints from an Indeterminate structure making it statically determinate is called primary structure. This is required for solving indeterminate structures by flexibility matrix method.
Write the formulae for degree of indeterminancy.
Γ Two dimensional in jointed truss (2D truss)
π=(π+π)β 2π
Γ Two dimensional rigid frames/plane rigid frames (2D frame)
π=(3π+π)β 3π
Γ Three dimensional space truss (3D truss)
π=(π+π)β 3π
Γ Three dimensional space frame (3D frame)
π=(6π+π)β 6π
Where,
m = number of members
r = number of reactions
j = number of joints
What is the effect of temperature on the members of a statically determinate plane truss?
In determinate structures temperature changes do not create any internal stresses. The changes in lengths of members may result in displacement of joints. But these would not result in internal stresses or changes in external reactions.
Define internal and external indeterminancy.
Internal indeterminacy (I.I) is the excess no of internal forces present in a member that make a structure indeterminate.
External indeterminacy (E.I) is the excess no of external reactions in the member that make a structure indeterminate.
Indeterminacy (i) = I.I + E.I
E.I = r β e; I.I = i β EI
Where,
r = no of support reactions and
e = equilibrium conditions
e = 3 (plane frames) and e = 6 (space frames)
What are the requirements to be satisfied while analyzing a structure?
Γ Equilibrium condition
Γ Compatibility condition
Γ Force displacement condition
Define degree of indeterminacy.
The excess number of reactions take make a structure indeterminate is called degree of indeterminancy. Indeterminancy is also called degree of redundancy.
Indeterminancy consists of internal and external indeterminancies. It is denoted by the symbol βiβ.
Degree of redundancy (i) = I.I + E.I
Where,
I.I = Internal indeterminancy
E.I =External indeterminancy
Differentiate the statically determinate structures and statically indeterminate structures.
STATICALLY DETERMINATE STRUCTURES
STATICALLY INDETERMINATE STRUCTURES
Conditions of equilibrium are sufficient to analyze the structure
Conditions of equilibrium are insufficient to analyze the structure
Bending moment and shear force is independent of material and cross sectional area
Bending moment and shear force is dependent of material and independent of cross sectional area
No stresses are caused due to
temperature change and lack of fit
Stresses are caused due to temperature change and lack of fit
Extra conditions like compatibility of displacements are not required to analyze the structure.
Extra conditions like compatibility of displacements are required to analyze the structure along with the equilibrium equations.
UNIT β 2
Distinguish between plane truss and plane frame. Plane frames are two-dimensional structures constructed with straight elements connected together by rigid and/or hinged connections. Frames are subjected to loads and reactions that lie in the plane of the structure.
If all the members of a truss and the applied loads lie in a single plane, the truss is called a plane truss.
What is meant by cambering technique in structures?
Cambering is a technique applied on site, in which a slight upward curve is made in the structure/beam during construction, so that it will straighten out and attain the straight shape during loading. This will considerably reduce the downward deflection that may occur at later stages.
Give the procedure for unit load method.
Γ Find the forces P1, P2, β¦β¦. in all the members due to external loads
Γ Remove the external loads and apply the unit vertical point load at the joint if the vertical deflection is required and find the stress
Γ Apply the equation for vertical and horizontal deflection
What are the assumptions made in unit load method?
Γ The external & internal forces are in equilibrium
Γ Supports are rigid and no movement is possible
Γ The materials are strained well within the elastic limit
Why is it necessary to compute deflections in structures?
Computation of deflection of structures is necessary for the following reasons:
Γ If the deflection of a structure is more than the permissible, the structure will not look aesthetic and will cause psychological upsetting of the occupants.
Γ Excessive deflection may cause cracking in the materials attached to the structure. For example, if the deflection of a floor beam is excessive, the floor finishes and partition walls supported on the beam may get cracked and unserviceable.
Define unit load method.
The external load is removed and the unit load is applied at the point, where the deflection or rotation is to found.
Distinguish between pin jointed and rigidly jointed structure.
PIN JOINTED STRUCTURE
RIGIDLY JOINTED STRUCTURE
The joints permit change of angle Between connected members.
The members connected at a rigid joint will maintain the angle between them even under deformation due to loads.
The joints are incapable of transferring Any moment to the connected members and vice-versa.
Members can transmit both forces and Moments between themselves through the joint.
The pins transmit forces between Connected members by developing shear.
Provision of rigid joints normally increases the redundancy of the structures.
What are the conditions of equilibrium?
The three conditions of equilibrium are the sum of horizontal forces, vertical forces and moments at any joint should be equal to zero.
(i.e.) Ξ£H = 0; Ξ£V = 0; Ξ£M = 0
Define trussed beam.
A beam strengthened by providing ties and struts is known as Trussed Beams.
Define βdeckβ and βthroughβ type truss.
A deck type is truss is one in which the road is at the top chord level of the trusses. We would not see the trusses when we ride on the road way.
A through type truss is one in which the road is at the bottom chord level of the trusses. When we travel on the road way, we would see the web members of the trusses on our left and right. That gives us the impression that we are going` throughβ the bridge.
What is meant by lack of fit in a truss?
One or more members in a pin jointed statically indeterminate frame may be a little shorter or longer than what is required. Such members will have to be forced in place during the assembling. These are called members having Lack of fit. Internal forces can develop in a redundant frame (without external loads) due to lack of fit.
Give any two situations where sway will occur in portal frames.
Γ Eccentric or Unsymmetrical loading
Γ Non-uniform section of the members
What are the different types of forces acts on a frame?
Γ Dynamic load
Γ Static load
What is meant by settlement of supports?
Support sinks mostly due to soil settlement. Rotation of βfixedβ ends can happen either because of soil settlement or upheaval of horizontal or
inclined fixed ends. Fixed end moments induced in beam ends because of settlement or rotation of supports.
What is a rigid joint?
The members connected at a rigid joint will maintain the angle between them even under deformation due to loads. Members can transmit both forces and moments between themselves through the joint. Provision of rigid joints normally increases the redundancy of the structures.
Write down the assumptions made in portal method.
Γ The point of contra-flexure in all the members lies at their middle points
Γ Horizontal shear taken by each interior column is double the horizontal shear taken by each of exterior column
Write down the assumptions made in cantilever method.
Γ The point of contra-flexure in all the members lies at their middle points
Γ The direct stress or axial stress in the columns due to horizontal forces, are directly proportional to their distance from the centroidal vertical axis of the frame
What are the methods used to analyze the beam when it settle at supports?
Γ Kaniβs method
Γ Moment distribution method
Γ Slope deflection method
Differentiate symmetry and anti-symmetry frames.
SYMMETRY FRAME
ANTI-SYMMETRY FRAME
For symmetric loading, Symmetric quantities like bending moment, displacements are symmetrical about the centroidal vertical axis.
For anti-symmetric loading, Symmetric quantities like bending moment, displacements are zero at the point of centroidal vertical axis.
Anti-symmetric quantities like slope and shear force are zero at the point of centroidal vertical axis.
Anti-symmetric quantities like slope and shear force are distributed about the centroidal vertical axis.
What is meant by thermal stress?
Thermal stresses are stresses developed in a structure/member due to change in temperature. Normally, determinate structures do not develop thermal stresses. They can absorb changes in lengths and consequent displacements without developing stresses.
Write any two important assumptions made in the analysis of trusses?
Γ The frame is a perfect frame
Γ The frame carries load at the joints
Γ All the members are pin-joined
Differentiate perfect and imperfect trusses?
The frame which is composed of such members, which are just sufficient to keep the frame in equilibrium, when the frame is supporting an external load, is known as perfect frame. Hence for a perfect frame, the number of joints and number of members are given by, π=2πβ3
A frame in which number of members and number of joints are not given by π=2πβ3 is known as imperfect frame. This means that number of members in an imperfect frame will be either more or less than 2πβ3
Write the difference between deficient and redundant frames?
If the number of members in a frame are less than (2πβ3), then the frame is known as deficient frame.
If the number of members in a frame are more than (2πβ3), then the frame is known as redundant frame.
UNIT β 3
What are the assumptions made in slope deflection method?
This method is based on the following simplified assumptions.
Γ All the joints of the frame are rigid, (i.e.) the angle between the members at the joints does not change, when the members of frame are loaded.
Γ Between each pair of the supports the beam section is constant.
Define fixed end moment.
The moments at the fixed joints of loaded member are called fixed end moment.
Write down the slope deflection equation for a fixed end support.
ππ΄π΅= ππΉπ΄π΅+ 2πΈπΌπ [ 2ππ΄+ ππ΅+ 3πΏπ ]
What are the moments induced in a beam member, when one end is given a unit rotation, the other end being fixed. What is the moment at the near end called?
When π=1, ππ΄π΅= 4 πΈπΌπ ,ππ΅π΄= 2 πΈπΌπ
ππ΄π΅ Is the stiffness of AB at B
Define the term sway.
Sway is the lateral movement of joints in a portal frame due to the unsymmetrical in dimensions, loads, moments of inertia, end conditions, etc. Sway can be prevented by unyielding supports provided at the beam level as well as geometric or load symmetry about vertical axis.
What are the situations where in sway will occur in portal frames?
Γ Eccentric or unsymmetrical loading
Γ Unsymmetrical geometry
Γ Different end conditions of the column
Γ Non-uniform section of the members
Γ Unsymmetrical settlement of supports
Γ A combination of the above
What are the symmetric and anti-symmetric quantities in structural behavior?
When a symmetrical structure is loaded with symmetrical loading, the bending moment and deflected shape will be symmetrical about the same axis. Bending moment and deflection are symmetrical quantities.
What is the ratio of sway moments at column heads when one end is fixed and the other end hinged? Assume that the length and M.I of both legs are equal.
Assuming the frame to sway to the right by Ξ΄
Ratio of sway moments = ππ΅π΄ππΆπ·= β ( 6 πΈπΌ πΏπ2 )β ( 3 πΈπΌ πΏπ2 )=2
A beam is fixed at its left end and simply supported at right. The right end sinks to a lower level by a distance βΞβ with respect to the left end. Find the magnitude and direction of the reaction at the right end if βlβ is the beam length and EI, the flexural rigidity.
ππ΄ (ππ’π π‘π π ππππππ ππ π΅)= 3 πΈπΌ πΏπ2
How many slope deflection equations are available for a two span continuous beam?
There will be 4 nos. of slope-deflection equations are available for a two span continuous beam.
What are the quantities in terms of which the unknown moments are expressed in slope-deflection method?
In slope-deflection method, unknown moments are expressed in terms of
Γ Slope (ΞΈ)
Γ Deflection (Ξ)
The beam shown in figure is to be analyzed by slope-deflection method. What are the unknowns and to determine them. What are the conditions used?
Unknowns: ππ΄,ππ΅,ππΆ
Equilibrium equations used:
Γ ππ΄π΅=0
Γ ππ΅π΄ + ππ΅πΆ=0
Γ ππΆπ΅=0
How do your account for sway in slope deflection method for portal frames?
Because of sway, there will be rotations in the vertical members of a frame. This causes moments in the vertical members. To account for this, besides the equilibrium, one more equation namely shear equation connecting the joint-moments is used.
Write down the equation for sway correction for the portal frame shown in figure.
πβπππ πππ’ππ‘πππ = ππ΄π΅ + ππ΅π΄π1 + ππΆπ· + ππ·πΆπ2 = 0
Who introduced slope-deflection method of analysis?
Slope-deflection method was introduced by Prof. George A. Maney in 1915.
Write down the equilibrium equations for the frame shown in figure.
Unknowns: ππ΅,ππΆ
Equilibrium equations used:
ππ΅π΄ + ππ΅πΆ = 0
ππΆπ΅ + ππΆπ· = 0
πβπππ πππ’ππ‘πππ = ππ΄π΅ + ππ΅π΄ β πβπ + ππΆπ· + ππ·πΆπ + π = 0
Write down the general slope-deflection equations and state what each term represents.
General slope deflection equations:
ππ΄π΅= ππΉπ΄π΅+ 2πΈπΌπ [ 2ππ΄+ ππ΅+ 3πΏπ ]
ππ΅π΄= ππΉπ΅π΄+ 2πΈπΌπ [ 2ππ΅+ ππ΄+ 3πΏπ ]
Where,
MFAB, MFBA = Fixed end moment at A and B respectively due to given loading
ππ΄,ππ΅ = Slopes at A and B respectively
πΏ = Sinking of support A with respect to B
How many slope-deflection equations are available for each span?
Two numbers of slope-deflection equations are available for each span, describing the moment at each end of the span.
In a continuous beam, one of the support sinks. What will happen to the span and support moments associated with the sinking of support.
Let support D sinks by πΏ. This will not affect span moments. Fixed end moments (support moments) will get developed as under
ππΉπΆπ· = ππΉπ·πΆ = β 6 πΈπΌ πΏπ12
ππΉπ·πΈ = ππΉπΈπ· = β 6 πΈπΌ πΏπ22
What is the basis on which the sway equation is formed for a structure?
Sway is dealt with in slope-deflection method by considering the horizontal equilibrium of the whole frame taking into account the shears at the base level of columns and external horizontal forces.
πβπ π βπππ ππππππ‘πππ ππ ππ΄π΅ + ππ΅π΄ β πβπ + ππΆπ· + ππ·πΆπ+ π=0
State the limitations of slope-deflection method.
Γ It is not easy to account for varying member sections
Γ It becomes very inconvenience when the unknown displacements are large in number
Γ This method is advantageous only for the structures with small Kinematic indeterminacy
Γ The solution of simultaneous equation makes the method tedious for annual computations
Why slope-deflection method is called a βdisplacement methodβ?
In slope-deflection method, displacements (like slopes and displacements) are treated as unknowns and hence the method is a βdisplacement methodβ.
Define Flexural rigidity of beams.
The product of youngβs modulus (E) and moment of inertia (I) is called Flexural Rigidity (EI) of Beams. The unit is Nmm2.
Define constant strength beam.
If the flexural Rigidity (EI) is constant over the uniform section, it is called Constant strength beam.
Define continuous beam.
A Continuous beam is one, which is supported on more than two supports. For usual loading on the beam hogging (- ive) moments causing convexity upwards at the supports and sagging (+ ive) moments causing concavity upwards occur at mid span.
What are the advantages of continuous beam over simply supported beam?
Γ The maximum bending moment in case of continuous beam is much less than in case of simply supported beam of same span carrying same loads.
Γ In case of continuous beam, the average bending moment is lesser and hence lighter materials of construction can be used to resist the bending moment.
UNIT β 4
Explain moment distribution method (Hardy cross method).
This method is first introduced by Professor Hardy Cross in 1932. It is widely used for the analysis of indeterminate structures. It uses an iterative technique. The method employs a few basic concepts and a few specialized terms such as fixed end moments, relative stiffness, carry over, distribution
factor. In this method, all the members of the structure are first assumed to be fixed in position and fixed end moments due to external loads are obtained.
Define distribution factor.
When several members meet at a joint and a moment is applied at the joint to produce rotation without translation of the members, the moment is distributed among all the members meeting at that joint proportionate to their stiffness.
π·ππ π‘ππππ’π‘πππ ππππ‘ππ= π
ππππ‘ππ£π π π‘ππππππ π ππ’π ππ πππππ‘ππ£π π π‘ππππππ π ππ‘ π‘βπ πππππ‘
If there are three members,
π·ππ π‘ππππ’π‘πππ ππππ‘πππ = π1π1+ π2+ π3,π2π1+ π2+ π3,π3π1+ π2+ π3
Define carry over factor.
A moment applied at the hinged end B βcarries overβ to the fixed end A, a moment equal to half the amount of applied moment and of the same rotational sense. C.O =0.5
What is the difference between absolute and relative stiffness?
Absolute stiffness is represented in terms of E, I and l, such as 4EI / l. Relative stiffness is represented in terms of βIβ and βlβ, omitting the constant E. Relative stiffness is the ratio of stiffness to two or more members at a joint.
In a member AB, if a moment of -10kN.m is applied at A, what is the moment carried over to B?
Carry over moment = Half of the applied moment
β΄ Carry over moment to B = -10/2 = -5 kN.m
Define Stiffness factor.
It is the moment required to rotate the end while acting on it through a unit rotation, without translation of the far end being ππππππ¦ π π’πππππ‘ππ ππ πππ£ππ ππ¦ (π)= 3 πΈπΌπ πΉππ₯ππ ππ πππ£ππ ππ¦ (π)= 4 πΈπΌπ
Where,
E = Youngβs modulus of the beam material
I = Moment of inertia of the beam
L = Beamβs span length
Define carry over moment.
It is defined as the moment induced at the fixed end of the beam by the action of a moment applied at the other end, which is hinged. Carry over moment is the same nature of the applied moment.
What is the sum of distribution factors at a joint?
Sum of distribution factors at a joint = 1.
What is the moment at a hinged end of a simple beam?
Moment at the hinged end of a simple beam is zero.
A rigid frame is having totally 10 joints including support joints. Out of slope-deflection and moment distribution methods, which method would you prefer for analysis? Why?
Moment distribution method is preferable.
If we use slope-deflection method, there would be 10 (or more) unknown displacements and an equal number of equilibrium equations. In addition, there would be 2 unknown support moments per span and the same number of slope-deflection equations. Solving them is difficult.
What are the limitations of moment distribution method? Γ This method is eminently suited to analyze continuous beams including non-prismatic members but it presents some difficulties when applied to rigid frames, especially when frames are subjected to side sway Γ Unsymmetrical frames have to be analyzed more than once to obtain FM (fixed moments) in the structures Γ This method cannot be applied to structures with intermediate hinges
UNIT β 5
What is the value of rotation moment at a fixed end considered in Kaniβs method?
ππ΄π΅=2πΈ πΎπ΄π΅ ππ΄ ππ΅π΄=2πΈ πΎπ΅π΄ ππ΅
What are the fundamental equations of Kaniβs method?
Ξ£πππ= Ξ£ππΉππ+ 2 Ξ£πππβ²+ Ξ£πππ=0 Ξ£πππβ²= β 12 ( Ξ£ππΉππ+ Ξ£πππβ² )
What are the limitations of Kaniβs method?
Γ Gasper Kani of Germany gave another distribution procedure in which instead of distributing entire moment in successive steps, only the rotation contributions are distributed
Γ Basic unknown like displacements which are not found directly
What are the advantages of Kaniβs method? Γ Hardy Cross method distributed only the unbalanced moments at joints, whereas Kaniβs method distributes the total joint moment at any stage of iteration Γ The more significant feature of Kaniβs method is that the process is self-corrective. Any error at any stage of iteration is corrected in subsequent steps Γ Framed structures are rarely symmetric and subjected to side sway, hence Kaniβs method is best and much simpler than other methods like moment distribution method and slope displacement method
State Miller-Breslau principle.
Miller-Breslau principle states that, if we want to sketch the influence line for any force quantity like thrust, shear, reaction, support moment or bending moment in a structure,
Γ We remove from the structure the resistant to that force quantity
Γ We apply on the remaining structure a unit displacement corresponding to that force quantity.
The resulting displacements in the structure are the influence line ordinates sought.
Define rotation factor.
Rotation factor in Kaniβs method is akin to distribution factor in moment distribution method.
Actually, π’ = β 0.5 Γ π·ππ π‘ππππ’π‘πππ ππππ‘ππ
Define displacement factor.
Ξππ Is the βdisplacement factorβ for each column, similar to π’ππ we adopted earlier for rotation factor. Actually, Ξππ = β1.5 π·πΉ and is applicable to column only.
Brief about Kaniβs method of analysis.
Kaniβs method of analyzing indeterminate structures, particularly, building frames was developed in Germany in the year 1947 by Dr. Gasper Kani. Like moment distribution it is a method of solving slope deflection equations by an iterative method. Hence, this will fall under the category of stiffness method wherein the level of difficulty would be decided by the degrees of freedom (and not the degree of redundancy).
What are the basic principles of compatibility?
Compatibility is defined as the continuity condition on the displacements of the structure after external loads are applied to the structure.
Define Kaniβs method and how it is better than MDM.
Kaniβs method is similar to the MDM in that both these methods use Gauss Seidel iteration procedure to solve the slope deflection equations, without explicitly writing them down. However the difference between
Kaniβs method and the MDM is that Kaniβs method iterates the member end moments themselves rather than iterating their increment Kaniβs method essentially consists of a single simple numerical operation performed repeatedly at the joints of a structure, in a chosen sequence.
Write the procedure for Kaniβs method.
While solving structures by this method the following steps may be kept in mind.
Γ Compute all fixed end moments
Γ Compute and tabulate all rotation factors for all joints that would have rotation.
Γ Fixed ends will not have rotation factors. Nor rotation contributions either to the same (fixed end) or to the opposite end.
Γ Extreme simply supported ends will initially get a fixed end moment.
Γ Iterative process can be formed.
(Or)
Γ Fixed end moment
Γ Rotation factor
Γ Resultant restraint moment
Γ Iteration cycle
Γ Final moment
What are the methods of analyzing building frame?
Γ Cantilever method
Γ Factor method
Γ Portal method
STRUCTURAL ANALYSIS β 2
UNIT β 1
What is an arch? Explain.
An arch is defined as a curved girder, having convexity upwards and supported at its ends. The supports must effectively arrest displacements in the vertical and horizontal directions only then there will be arch action.
State the general cable theorem.
The general cable theorem helps us determine the shape of a cable supported at two ends when it is acted upon by vertical forces. It can be stated as: βAt any point on a cable acted upon by vertical loads, the product of the horizontal component of cable tension and the vertical distance from that point to the cable chord equals the moment this would occur at that section if the loads carried by the cable were acting on an simply-supported beam of the same span as that of the cable.β
What are the various types of hinges in arch? (or) What are the types of arches according to the support conditions?
Γ Three hinged arch
Γ Two hinged arch
Γ Single hinged arch
Γ Fixed or hinge less arch
What are the types of arches according to their shapes?
Γ Curved arch
Γ Parabolic arch
Γ Elliptical arch
Γ Polygonal arch
Define horizontal thrust.
In a 3 hinged arch, the force H is calculated by equating the bending
moment at the central hinge to zero. The horizontal thrust H reduces the
beam bending moment called ΞΌx. π΄ππ‘π’ππππ¦ ππ ππ πππβ, ππ₯ = ππ₯ β π»π¦
What is a linear arch?
If an arch is to take loads, say W1, W2, and W3 and a vector diagram
and funicular polygon are plotted as shown in figure, the funicular polygon
is known as the linear arch or theoretical arch.
The polar distance βo tβ represents the horizontal thrust. The links
AC, CD, DE and EB will be under compression and there will be no bending
moment. If an arch of this shape ACDEB is provided, there will be no
bending moment.
For a given set of vertical loads W1, W2β¦β¦etc. we can have any
number of linear arches depending on where we chose βOβ or how much
horizontal thrust (o t) we choose to introduce.
Draw the influence line for horizontal reaction, H in a three hinged
stiffening girder.
Why stiffening girders are necessary in the suspension bridges?
Γ Stiffening girders enable the suspension bridge decks to remain fairly
level
Γ Whatever be the live load on the deck slab, the stiffening girders will
convert and transmit the load on the deck slab as a uniformly
distributed load and thereby help the cable retain the parabolic shape
during the passage of loads
Γ The dead load of the girders which is a UDL is directly transmitted to
the cables and is taken up entirely by the tension in the cables
Γ Thus the uniformly distributed dead load will not cause any shear
force or bending moment in the stiffening girder
Γ The stiffening girders will have to resist the Shear force and bending moment due to live loads
Write the expression for horizontal thrust in a three hinged parabolic arch carrying UDL over entire span.
π»= π€ π28π¦π
Write the expression for horizontal thrust of a semicircular arch.
π»= π cos2π·π
If the load is applied at the centre, we get π»= ππ=0.318 π
A flexible cable 20m long is supported at two ends at the same level. The supports are 16m apart. Determine the dip of the cable.
GIVEN DATA:
S = 20m
l = 16m
TO FIND:
d =?
SOLUTION: π=π+ 83 π2π
π = β
( π β π ) Γ 3π
8
d = 4.89m
State the βEddyβs theoremβ for an arch.
Eddyβs theorem states that the bending moment at any section of an
arch is equal to the vertical intercept between the linear arch and the center
line of the actual arch.
π΅ππ₯ = πππππππ‘π π2π3 Γ π ππππ ππππ‘ππ
Explain with the aid of a sketch the normal thrust and radial shear in
an arch rib.
Let us take a section X of an arch. Let q be the inclination of the tangent at X. If H is the horizontal thrust and V is the vertical shear at X, from the free body of the RHS of the arch, it is clear that V and H will have normal and radial components given by, π
πππππ π βπππ ( π
π₯ )= ππ₯cosπβ π»sinπ ππππππ π‘βππ’π π‘ ( ππ₯ )= ππ₯sinπ+ π»cosπ
What is the static indeterminacy of a three hinged parabolic arch?
For a three hinged parabolic arch, the degree of static indeterminacy is zero. It is statically determinate.
Which of the two arches, viz. circular and parabolic is preferable to carry a uniformly distributed load? Why?
Parabolic arches are preferably to carry distributed loads. Because, both the shape of the arch and the shape of the bending moment diagram are parabolic. Hence the vertical intercept between the theoretical arch and actual arch is zero everywhere. Hence, the bending moment at every section of the arch will be zero. The arch will be under pure compression which will be economical.
What is the difference between the basic action of an arch and suspension cable?
An arch is essentially a compression member which can also take bending moments and shears. Bending moments and shears will be absent if the arch is parabolic and the loading uniformly distributed.
A cable can take only tension. A suspension bridge will therefore have a cable and a stiffening girder. The girder will take the bending moment and shears in the bridge and the cable, only tension.
Because of the thrusts in the cables and arches, the bending moments are considerably reduced.
If the load on the girder is uniform, the bridge will have only cable tension and no bending moment on the girder.
Under what conditions will the bending moment in an arch be zero throughout?
The bending moment in an arch throughout the span will be zero, if
Γ The arch is parabolic
Γ The arch carries UDL throughout the span
Indicate the positions of a moving point load for maximum negative and positive bending moments in a three hinged arch.
Considering a three hinged parabolic arch of span βlβ and subjected to a moving point load W, the position of the point load for
Γ Maximum negative bending moment is 0.25l from end supports.
Γ Maximum positive bending moment is 0.211l from end supports.
What are cable structures?
Long span structures subjected to tension and uses suspension cables for supports. Examples of cable structures are suspension bridges, cable stayed roof.
Draw the ILD for bending moment at a section x at a distance x from
the left end of a three hinged parabolic arch of span βlβ and rise βhβ.
ππ₯ = ππ₯ β π»π¦
Distinguish between two hinged and three hinged arches.
TWO HINGED ARCHES THREE HINGED ARCHES
Statically indeterminate to first
degree
Statically determinate
Might develop temperature stresses Increase in temperature causes
increase in central rise. No stresses
Structurally more efficient Easy to analysis. But in
construction, the central hinge may
involve additional expenditure.
Will develop stresses due to sinking
of supports
Since this is determinate, no stresses
due to support sinking.
Explain rib shortening in the case of arches.
In a two hinged arch, the normal thrust which is a compressive force
along the axis of the arch will shorten the rib of the arch. This in turn will
release part of the horizontal thrust. Normally, this effect is not considered in
the analysis (in the case of two hinged arches).
Depending upon the importance of the work we can either take into account or omit the effect of rib shortening. This will be done by considering (or omitting) strain energy due to axial compression along with the strain energy due to bending in evaluating H.
Explain the yielding of support in the case of an arch.
Yielding of supports has no effect in the case of a 3 hinged arch which is determinate. These displacements must be taken into account when we analyze 2 hinged or fixed arches under
ππππ»= Ξπ» Instead of zero
πππππ΄= Ξππ΄ Instead of zero
Here U is the strain energy of the arch and ΞH and ΞVA are the displacements due to yielding of supports.
Write the formula to calculate the change in rise in three hinged arch.
πΆβππππ ππ πππ π=( π2+ 4π¦π24π¦π ) Γ πΌπ
Where,
l = span length of the arch
yc = central rise of the arch
Ξ± = coefficient of thermal expansion
T = change in temperature
In a parabolic arch with two hinges how will you calculate the slope of the arch at any point?
πππππ ππ πππππππππ πππβ ( π )= tanβ1( 4π¦ππ2 Γ( πβ2π₯ ))
Where,
ΞΈ = slope at any point x (or) inclination of tangent at x
l = span length of the arch
yc = central rise of the arch
How will you calculate the horizontal thrust in a two hinged parabolic arch if there is a rise in temperature?
π»ππππ§πππ‘ππ π‘βππ’π π‘ ( π» )= πΌ π π πΈ πΌβ«π¦2 ππ₯π0
Where,
l = span length of the arch
y = rise of the arch at any point x
Ξ± = coefficient of thermal expansion
T = change in temperature
E = Youngβs Modulus of the material of the arch
I = Moment of Inertia
What is the true shape of cable structures?
Cable structures especially the cable of a suspension bridge is in the form of a catenary. Catenary is the shape assumed by a string / cable freely suspended between two points.
What is the nature of force in the cables?
Cables of cable structures have only tension and no compression or bending.
What is a catenary?
Catenary is the shape taken up by a cable or rope freely suspended between two supports and under its own self weight.
Mention the different types of cable structures?
Γ Cable over a guide pulley
Γ Cable over a saddle
Briefly explain cable over a guide pulley.
Cable over a guide pulley has the following properties:
Γ Tension in the suspension cable = tension in the anchor cable
Γ The supporting tower will be subjected to vertical pressure and bending due to net horizontal cable tension
Briefly explain cable over saddle.
Cable over saddle has the following properties:
Γ Horizontal component of tension in the cable = horizontal component of tension in the anchor cable
Γ The supporting tower will be subjected to only vertical pressure due to cable tension
What are the main functions of stiffening girder in suspension bridges?
Γ They help in keeping the cables in shape
Γ They resist part of the Shear force and bending moment due to live loads
What is the degree of indeterminacy of a suspension bridge with two hinged stiffening girder?
The two hinged stiffening girder has one degree of indeterminacy.
Give some examples of beams curved in plan.
Curved beams are found in the following structures.
Γ Beams in the bridge negotiating a curve
Γ Ring beams supporting a water tank
Γ Beams supporting corner lintels
Γ Beams in ramps
Differentiate between plane truss and space truss.
PLANE TRUSS
SPACE TRUSS
All members lie in one plane
This is a three dimensional truss
All joints are assumed to be hinged
All joints are assumed to be ball and socketed
Give some examples of beams curved in plan.
Curved beams are found in the following structures.
Γ Beams in the bridge negotiating a curve
Γ Ring beams supporting a water tank
Γ Beams supporting corner lintels
Γ Beams in ramps
What are the forces developed in beams curved in plan?
Beams curved in plan will have the following forces developed in them.
Γ Bending moments
Γ Shear forces
Γ Torsional moments
Define tension coefficient of a truss member.
The tension coefficient for a member of a truss is defined as the pull or tension in the member divided by its length (i.e.) the force in the member per unit length.
What are the significant features of circular beams on equally spaced supports?
Γ Slope on either side of any support will be zero
Γ Torsional moment on every support will be zero
Give the expression for calculating equivalent UDL on a girder.
ππ= π‘ππ‘ππ ππππ ππ πππππππ πππ ππ ππππππ
Give the expression for determining the tension T in the cable.
The tension developed in the cable is given by, π= βπ»2+ π2
Where,
H = horizontal component
V = vertical component
What are cables made of?
Cables can be of mild steel, high strength steel, stainless steel, or
polyester fibres. Structural cables are made of a series of small strands
twisted or bound together to form a much larger cable. Steel cables are either
spiral strand, where circular rods are twisted together or locked coil strand,
where individual interlocking steel strands form the cable (often with a spiral
strand core).
Spiral strand is slightly weaker than locked coil strand. Steel spiral
strand cables have a Young’s modulus, E of 150 Β± 10 kN/mmΒ² and come in
sizes from 3 to 90 mm diameter. Spiral strand suffers from construction
stretch, where the strands compact when the cable is loaded.
Give the horizontal and vertical components of a cable structure
subjected to UDL.
The horizontal and vertical reactions are given by,
π» =
π€ π2
8π
And π =
π€ π
2
What is meant by βReaction locusβ for a two hinged arch?
The Reaction locus is a line which gives the point of intersection of
the two reactions for any position of an isolated load.
Give the range of central dip of a cable.
The central dip of a cable ranges from 1/10 to 1/12 of the span.
Give the types of significant cable structures.
Γ Linear structure
Β· Suspension bridges
Β· Draped cables
Β· Cable stayed beams or trusses
Β· Cable trusses
Β· Straight tensioned cables
Γ Three dimensional structure
Β· Bicycle wheel roof
Β· 3D cable trusses
Β· Tensegrity structures
Β· Tensairity structures
UNIT β 2 & 3
Where do you get the rolling loads in practice?
Shifting of load positions is common enough in buildings. But they are more pronounced in bridges and in gantry girders over which vehicles keep rolling.
List the categories of rolling loads on beams.
Γ Single concentrated load
Γ UDL longer than the beam span
Γ UDL shorter than the beam span
Γ Two wheel axles separated by a fixed distance
Γ Multiple wheel axles (train of loads)
What are the objectives of study on rolling loads?
Γ To find the load position and values of maximum shear force and bending moment at a given section due to a given system of rolling loads
Γ To find the location and values of the absolute maximum shear force and bending moment that may occur on the span due to the given system of rolling loads
Γ To find the equivalent UDL due to a given system of rolling loads to make the designerβs work simple
Name the type of rolling loads for which the absolute bending moment occurs at the mid span of a beam.
Single concentrated load, UDL longer than the span, UDL shorter than the span Also when the resultant of several concentrated loads crossing a span, coincides with a concentrated load then also the maximum bending moment occurs at the centre of the span.
Where do you have the absolute maximum bending moment in a simply supported beam when a series of wheel loads cross it?
When a series of wheel loads crosses a simply supported beam, the absolute maximum bending moment will occur near mid span under the load Wcr, nearest to mid span (or the heaviest load). If Wcr is placed to one side of mid span C, the resultant of the load system R shall be on the other side of C and Wcr and R shall be equidistant from C. Now the absolute maximum
bending moment will occur under Wcr. If Wcr and R coincide, the absolute maximum bending moment will occur at mid span.
What is the absolute maximum bending moment due to a UDL longer than the span of a simply supported beam?
When a simply supported beam is subjected to a moving UDL longer than the span, the absolute maximum bending moment occurs when the whole span is loaded. πmax πππ₯= π€ π28
State the location of a maximum shear force in a simple beam with any kind of loading.
In a simple beam with any kind of load, the maximum positive Shear force occurs at the left hand support and maximum negative Shear force occurs at right hand support.
What is meant by absolute maximum bending moment in a beam?
When a given load system moves from one end to the other end of a girder, depending upon the position of the load, there will be a maximum bending moment for every section. The maximum of these bending moments will usually occur near or at the mid span. The maximum of maximum bending moments is called the absolute maximum bending moment.
What is meant by influence lines?
An influence line is a graph showing, for any given frame or truss, the variation of any force or displacement quantity (such as shear force, bending moment, tension, deflection) for all positions of a moving unit load as it crosses the structure from one end to the other.
An influence line for any given point or section of structure is a curve whose ordinates represent to scale the variation of a function, such as shear force, bending moment, deflection etc. at the point or section, as the unit load moves across the structure. ILD for determinate beam is linear and for indeterminate structure is curvilinear.
What are the uses of influence diagrams?
Γ Influence lines are very useful in the quick determination of reactions, shear force, bending moment or similar functions at a given section under any given system of moving loads and
Γ Influence lines are useful in determining the load position to cause maximum value of a given function in a structure on which load positions can vary.
State Muller Breslau principle.
Muller-Breslau principle states that, if we want to sketch the influence line for any force quantity (like thrust, shear, and reaction, support moment or bending moment) in a structure,
Γ We remove from the structure the restraint to that force quantity and
Γ We apply on the remaining structure a unit displacement corresponding to that force quantity.
The resulting displacements in the structure are the influence line ordinates sought.
Write the uses of Muller Breslau principle.
Γ It is the most important tool in obtaining influence lines for statically determinate as well as statically indeterminate structures
Γ It is used as the straight application of Maxwellβs reciprocal theorem
Define the term βEquivalent uniformly distributed loadβ.
A given system of loading crossing a girder or structure can always be replaced by a uniformly distributed load longer than the span. Such that the B.M or S.F due to the static load everywhere is at least equal to the caused by the actual system of moving loads. Such a static load is known as Equivalent Uniformly Distributed Load.
What is the necessity of model analysis?
Γ When the mathematical analysis of problem is virtually impossible
Γ Mathematical analysis though possible is so complicated and time consuming that the model analysis offers a short cut
The importance of the problem is such that verification of mathematical analysis by an actual test is essential.
What do you understand by the term reversal of stresses?
In certain long trusses the web members can develop either tension or compression depending upon the position of live loads. This tendency to change the nature of stresses is called reversal of stresses.
A single load of W rolls along a girder of span βlβ. Draw the diagrams of
maximum bending moment and shear force.
Draw the ILD for shear force shear force at a point x in a simply
supported beam AB of span l.
State Maxwell β Bettiβs theorem.
In a linearly elastic structure in static equilibrium acted upon by either
of two systems of external forces, the virtual work done by the first system
of forces in undergoing the displacements caused by the second system of
forces is equal to the virtual work done by the second system of forces in
undergoing the displacements caused by the first system of forces.
Maxwell Bettiβs theorem helps us to draw influence lines for structures.
Draw the influence line for radial shear at a section of a three hinged
arch.
π
πππππ π βπππ ( π
π₯ ) = ππ₯ cos π β π» sin π
Where, ΞΈ is the inclination of tangent at x
Draw the ILD for bending moment at any section x of a simply
supported beam and mark the ordinates.
Sketch the ILD for the normal thrust at a section X of a symmetric
three hinged parabolic arch.
ππππππ π‘βππ’π π‘ ( ππ₯ ) = ππ₯ sin π + π» cos π
Where, ΞΈ is the inclination of tangent at x
What is meant by maximum shear force diagram in influence line?
Due to a given system of rolling loads the maximum shear force for
every section of the girder can be worked out by placing the loads in
appropriate positions. When these are plotted for all the sections of the
girder, the diagram that we obtain is the maximum shear force diagram. This diagram yields the βdesign shearβ for each cross section.
Define Maxwellβs reciprocal theorem or Betteβs theorem.
The work done by the first system of loads due to displacements caused by a second system of loads equals to the work done by the second system of loads due to displacements caused by the first system of loads.
Define similitude.
Similitude means similarity between two objects namely the model and the prototype with regard to their physical characteristics.
Γ Geometric similitude is similarity of form
Γ Kinematic similitude is similarity of motion
Γ Dynamic and / or mechanical similitude is similarity of masses and / or forces
State the principle on which indirect model analysis is based.
The indirect model analysis is based on the Muller Breslau principle.
Muller Breslau principle has led to a simple method of using models of structures to get the influence lines for force quantities like bending moments, support moments, reactions, internal shears, thrusts, etc.
To get the influence line for any force quantity,
Γ Remove the restraint due to the force
Γ Apply a unit displacement in the direction of the force
Γ Plot the resulting displacement diagram
This diagram is the influence line for the force.
What is the principle of dimensional similarity?
Dimensional similarity means geometric similarity of form. This means that all homologous dimensions of prototype and model must be in some constant ratio.
What is Beggβs deformeter?
Beggβs deformeter is a device to carry out indirect model analysis on structures. It has the facility to apply displacement corresponding to moment, shear or thrust at any desired points in the model. In addition, it provides facility to measure accurately the consequent displacements all over the model.
Name any four model making materials.
Perspex, Plexiglas, acrylic, plywood, sheet araldite and Bakelite are some of the model making materials. Micro β concrete, mortar and plaster of Paris can also be used for models.
What is dummy length in models tested with Beggβs deformeter?
Dummy length is the additional length (of about 10 to 12mm) left at the extremities of the model to enable any desired connection to be made with the gauges.
What are the three types of connections possible with the model used with Beggβs deformeter?
Γ Hinged connection
Γ Fixed connection
Γ Floating connection
What are the uses of a micrometer microscope in model analysis with Beggβs deformeter?
Micrometer microscope is an instrument used to measure the displacement of any point in the x and y directions of a model during tests with Beggβs deformeter.
UNIT β 4
What is meant by yield stress?
Most structural materials have under gradually increasing strain an elastic and plastic stage.
Plastic stage mark the stage at which increased strain does not produce in stress.
The stress consequent to stretching stabilize at a value is known as yield stress.
What are the basic conditions to be satisfied for plastic analysis?
Γ Mechanism condition
The ultimate load or collapse load is reached when a mechanism is formed. There must, however, be just enough plastic hinges that a mechanism is formed.
Γ Equilibrium condition
The summation of the forces and moments acting on a structure must be equal to zero.
Γ Plastic moment condition
The bending moment anywhere must not exceed the fully plastic moment.
What are the basic conditions to be satisfied for elastic analysis?
Γ Continuity equation
Γ Equilibrium condition
Γ Limiting stress condition
List out the shape factors for the rectangular, triangular, circular and diamond section.
Γ Rectangular section, S = 1.5
Γ Triangular section, S = 2.346
Γ Circular section, S = 1.697
Γ Diamond section, S = 2
Mention the types of frames.
Γ Symmetric frames
Γ Un-symmetric frames
What are symmetric frames and how they analyzed?
Symmetric frames are frames having the same support conditions, lengths and loading conditions on the columns and beams of the frame. Symmetric frames can be analyzed by,
Γ Beam mechanism
Γ Column mechanism
What are unsymmetrical frames and how they analyzed?
Unβsymmetric frames have different support conditions, lengths and loading conditions on its columns and beams. These frames can be analyzed by,
Γ Beam mechanism
Γ Column mechanism
Γ Panel or sway mechanism
Γ Combined mechanism
What is the effect of axial force on plastic moment when a section is subjected to axial force?
Thus far the cross sections considered are only carrying moment. In the presence of axial force, clearly some material must be given over to carry the axial force and so is not available to carry moment, reducing the capacity of the section. Further, it should be apparent that the moment capacity of the section therefore depends on the amount of axial load being carried. Considering a compression load as positive, more of the section will be in compression and so the neutral axis will drop.
Draw a stress strain curve for a perfectly plastic material.
What is a mechanism?
When an n-degree indeterminate structure develops n plastic hinges, it becomes determinate and the formation of an additional hinge will reduce the structure to a mechanism. Once a structure becomes a mechanism, it will collapse.
What are the different types of mechanism?
Γ Beam mechanism
Γ Column mechanism
Γ Panel or sway mechanism
Γ Gable mechanism
Γ Combined or composite mechanism
What are the methods of plastic analysis?
Γ Static method (Lower Bound Theorem)
Γ Kinematic method (Upper Bound Theorem)
State the lower bound theorem or static theorem of plastic collapse.
Lower bound theory states that the collapse load is determined by assuming suitable moment distribution diagram.
The moment distribution diagram is drawn in such a way that the conditions of equilibrium are satisfied.
State upper bound theorem of plasticity.
Upper bound theory states that of all the assumed mechanisms the exact collapse mechanism is that which requires a minimum load.
Define shape factor.
The shape factor (S) is defined as the ration of the plastic moment of a section to the yielded moment of the section. The shape factor is also the ratio of plastic modulus of the section to the elastic modulus of the section. π= ππππ¦= πππ
Define the term load factor.
Plastic analysis can tell us at what load (or load combination) a structure will collapse. This will help us design structures for a desired safety factor on limiting loads. This safety factor is usually termed as load factor. It is also defined as the ratio of collapse load to the working load.
π= πππ
Define collapse load.
The load that causes the (n + 1) the hinge to form a mechanism is called collapse load where n is the degree of statically indeterminacy. Once the structure becomes a mechanism it will collapse.
What are the limitations of load factor?
Γ The analysis procedure does not give us any clue if at a loadππ’ Γ·ππππ ππππ‘ππ, the structure behaves well, meaning, whether the stresses are within limit. So we have to check the stresses at crucial points by conventional elastic method
Γ The assumption of monotonic increase in loading is a simplistic, native assumption. But it is convenient and so we stick to it.
Explain the term plastic hinge.
When a section attains full plastic moment Mp, it acts as hinge which is called a plastic hinge.
It is defined as the yielded zone due to bending at which large rotations can occur with a constant value of plastic moment Mp.
What is plastic moment?
When the moment is further increased, there will be a stage at which all fibres from top to bottom of the section will completely yield and the section would not be able to take any further moment. The resisting moment corresponding to this fully plastic stage is called the plastic moment Mp.
Define plastic modulus of a section.
The plastic modulus of a section is the first moment of the area above and below the equal area axis. It is the resisting modulus of a fully plasticized section. ππ= π΄2 ( π¦1+ π¦2 )
List the possible locations of plastic hinges in a structure.
Γ Plastic hinges occurs under the loads
Γ Plastic hinges occurs at joints
Define moment redistribution.
Moment redistribution refers to the behavior of statically indeterminate structures that are not completely elastic, but have some reserve plastic capacity.
How is the shape factor for a hollow circular section related to the shape factor of an ordinary circular section?
The shape factor of the hollow circular section = a factor K * shape factor of ordinary circular section. πβπππ ππππ‘ππ ππ βπππππ€ πππππ’πππ π πππ‘πππ=π βπππ ππππ‘ππ ππ πππππ’πππ π πππ‘πππ Γ ( 1β π3 )( 1β π4 )
Give the governing equation for bending.
The governing equation for bending is given by, ππΌ= ππ¦
Where,
M = bending moment
I = moment of inertia
Ο = stress
y = CG distance
What is meant by plastic analysis of structure?
The analysis of beams and structures made of such flexural members are called plastic analysis of structure.
What is the difference between plastic hinge and mechanical hinge?
Plastic hinges modify the behavior of structures in the same way as mechanical hinges. The only difference is that plastic hinges permit rotation with a constant resisting moment equal to the plastic moment Mp. At mechanical hinges, the resisting moment is equal to zero.
List out the assumptions made for plastic analysis.
Γ Plane transverse sections remain plane and normal to the longitudinal axis before and after bending
Γ Effect of shear is neglected
Γ The material is homogeneous and isotropic both in the elastic and plastic state
Γ Modulus of elasticity has the same value both in tension and compression
Γ There is no resultant axial force in the beam
Γ The cross section of the beam is symmetrical about an axis through its centroid and parallel to the plane of bending
UNIT β 5
State the principle of super position of forces?
When a body is subjected to a number of external forces, the forces are split up, and their effects are considered on individual sections. The resulting deformation, of the body is equal to the algebraic sum of the deformations of the individual sections. Such a principle of finding the resultant deformation is called the principle of superposition.
Define statically determinate structure.
If the conditions of equilibrium (i.e.) Ξ£H=0, Ξ£V=0 and Ξ£M=0 alone are sufficient to find either external reactions or internal forces in a structure, the structure is called a statically determinate structure.
Define statically indeterminate structure.
If the conditions of equilibrium (i.e.) Ξ£H=0, Ξ£V=0 and Ξ£M=0 alone are not sufficient to find either external reactions or internal forces in a structure, the structure is called a statically indeterminate structure.
Differentiate the statically determinate structures and statically indeterminate structures.
STATICALLY DETERMINATE STRUCTURES
STATICALLY INDETERMINATE STRUCTURES
Conditions of equilibrium are sufficient to analyze the structure
Conditions of equilibrium are insufficient to analyze the structure
Bending moment and shear force is independent of material and cross sectional area
Bending moment and shear force is dependent of material and independent of cross sectional area
No stresses are caused due to
temperature change and lack of fit
Stresses are caused due to temperature change and lack of fit
Extra conditions like compatibility of displacements are not required to analyze the structure.
Extra conditions like compatibility of displacements are required to analyze the structure along with the equilibrium equations.
Write down the rotation matrix for 2D truss element.
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix
Define compatibility in force method of analysis.
Compatibility is defined as the continuity condition on the displacements of the structure after external loads are applied to the structure.
Write down the compatibility equation used in flexibility matrix method.
π
Γ Ξ = {πΉ}
Define force transformation matrix.
The connectivity matrix which relates the internal forces Q and the external forces R is known as the force transformation matrix. Writing it in a matrix form,
{Q} = [b] {R}
Where,
Q = member force matrix / vector
b = force transformation matrix
R = external force / load matrix / vector
What is transformation matrix?
If, A and B are the matrices of two linear transformations, then the effect of applying first A and then B to a vector x is given by: (This is called the associative property.) In other words, the matrix of the combined
transformation A followed by B is simply the product of the individual
matrices.
Write down the stiffness matrix for 2D beam element.
The stiffness matrix for a 2 D beam element is given by,
Describe the uses of force method. What are the basic steps in the force
method to find internal forces in statically indeterminate structure?
With the advent of computers, matrix methods of solving structures
have become very popular. The behavior of a structure can largely be
defined by defining the force β displacement relationship in the form of a
matrix.
Steps:
Γ Applying a force on the structure
Γ Working out the internal forces and moments
Γ Computing displacement (and rotations) at specific locations making
use of the values in the above step.
What are the basic unknowns in stiffness matrix method?
In the stiffness matrix method nodal displacements are treated as the
basic unknowns for the solution of indeterminate structures.
Define stiffness coefficient kij.
Stiffness coefficient βkijβ is defined as the force developed at joint βiβ due to unit displacement at joint βjβ while all other joints are fixed.
What is the basic aim of the stiffness method?
The aim of the stiffness method is to evaluate the values of generalized coordinates βrβ knowing the structure stiffness matrix βkβ and nodal loads βRβ through the structure equilibrium equation.
{R} = [K] {r}
What is the displacement transformation matrix?
The connectivity matrix which relates the internal displacement βqβ and the external displacement βrβ is known as the displacement transformation matrix βaβ.
{q} = [a] {r}
How are the basic equations of stiffness matrix obtained?
The basic equations of stiffness matrix are obtained as:
Γ Equilibrium forces
Γ Compatibility of displacements
Γ Force displacement relationships
What is the equilibrium conditions used in the stiffness method?
The external loads and the internal member forces must be in equilibrium at the nodal points.
What is meant by generalized coordinates?
For specifying a configuration of a system, a certain minimum no of
independent coordinates are necessary. The least no of independent
coordinates that are needed to specify the configuration is known as
generalized coordinates.
Write the element stiffness for a truss element.
The element stiffness matrix for a truss element is given by,
Write about the force displacement relationship.
The relationship of each element must satisfy the stress-strain
relationship of the element material.
What is the compatibility condition used in the flexibility method?
The deformed elements fit together at nodal points.
Write the element stiffness matrix for a beam element.
The element stiffness matrix for a beam element is given by,
Is it possible to develop the flexibility matrix for an unstable structure?
In order to develop the flexibility matrix for a structure, it has to be
stable and determinate.
Compare flexibility method and stiffness method.
FLEXIBILITY MATRIX METHOD
STIFFNESS MATRIX METHOD
The redundant forces are treated as basic unknowns.
The joint displacements are treated as basic unknowns
The number of equations involved is equal to the degree of static indeterminacy of the structure.
The number of displacements involved is equal to the no of degrees of freedom of the structure
The method is the generalization of consistent deformation method.
The method is the generalization of the slope deflection method.
Different procedures are used for determinate and indeterminate structures
The same procedure is used for both determinate and indeterminate structures.
What is the relationship between flexibility and stiffness matrix?
The element stiffness matrix βkβ is the inverse of the element flexibility matrix βfβ and is given by f = 1/k or k = 1/f.
What are the types of structures that can be solved using stiffness matrix method?
Structures such as simply supported, fixed beams and portal frames can be solved using stiffness matrix method.
Give the formula for the size of the global stiffness matrix.
The size of the Global Stiffness Matrix (GSM) = number of nodes * degrees of freedom per node.
List the properties of the stiffness matrix.
Γ It is a square matrix and always it should be a square matrix.
Γ It is a symmetric matrix
[π]= [π]π
Γ The sum of elements in any column must be equal to zero.
Γ It is an unstable element therefore the determinant is equal to zero.
Γ The order of stiffness is equal to the number of co β ordinates.
List the properties of flexibility matrix.
Γ Flexibility matrix is a square matrix of order nd nd
Γ Flexibility matrix is a symmetrical matrix
Γ Elements of flexibility matrix may be positive or negative except leading diagonal element which is always positive
Γ Elements of flexibility matrix are displacements and they can be computed only if the structure is stable. If structure is unstable internally or externally, then displacements are indefinitely large and flexibility matrix does not exist.
Why the stiffness matrix method is also called equilibrium method or displacement method?
Stiffness method is based on the superposition of displacements and hence is also known as the displacement method. And since it leads to the equilibrium equations the method is also known as equilibrium method.
Define a primary structure.
A structure formed by the removing the excess or redundant restraints from an indeterminate structure making it statically determinate is called primary
structure. This is required for solving indeterminate structures by flexibility
matrix method.
If the flexibility matrix is given as[π] = [
π βπ
βπ π
]. Write the
corresponding stiffness matrix.
ππ‘ππππππ π πππ‘πππ₯ =
1
πΉπππ₯ππππππ‘π¦ πππ‘πππ₯
(i.e.) [πΎ] = [πΉ]β1
Define degree of kinematic indeterminacy (or) Degree Of Freedom.
It is defined as the least no of independent displacements required to
define the deformed shape of a structure. There are two types of DOF
Γ Joint type DOF
Γ Nodal type DOF
Name any two force methods to analyze the statically indeterminate
structures.
Γ Column analogy method
Γ Flexibility matrix method
Γ Method of consistent deformation
Γ Theorem of least work
Briefly explain the two types of DOF.
Γ Joint type DOF
This includes the DOF at the point where moment of inertia changes, hinge and roller support, and junction of two or more members.
Γ Nodal type DOF
This includes the DOF at the point of application of concentrated load or moment, at a section where moment of inertia changes, hinge support, roller support and junction of two or more members.
What are the different methods used to analyze indeterminate structures?
Γ Finite element method
Γ Flexibility matrix method
Γ Stiffness matrix method
Write the formulae for degree of indeterminancy.
Γ Two dimensional in jointed truss (2D truss)
π=(π+π)β 2π
Γ Two dimensional rigid frames/plane rigid frames (2D frame)
π=(3π+π)β 3π
Γ Three dimensional space truss (3D truss)
π=(π+π)β 3π
Γ Three dimensional space frame (3D frame)
π=(6π+π)β 6π
Where,
m = number of members
r = number of reactions
j = number of joints
Write the element flexibility matrix for a truss member.
The element flexibility matrix (f) for a truss member is given by,
Briefly mention the two types of matrix methods of analysis of
indeterminate structures.
Γ Flexibility matrix method
It is defined as the deformation produced for unit load. It is denoted
by the symbols[π] ππ [π] ππ [πΌ]. This method is also called the force
method in which the forces in the structure are treated as unknowns.
The no of equations involved is equal to the degree of static
indeterminacy of the structure.
Γ Stiffness matrix method
It is defined as the force required for unit deformations. It is denoted
by the symbol[π]. This is also called the displacement method in
which the displacements that occur in the structure are treated as
unknowns. The no of displacements involved is equal to the no of
degrees of freedom of the structure.
Define flexibility influence coefficient.
Flexibility influence coefficient (fij) is defined as the displacement at
joint βiβ due to a unit load at joint βjβ, while all other joints are not load.
Define element co β ordinates.
Each element having a displacement along two directions (x and y) is
said to be an element coordinates.
Define global co β ordinates.
For the whole structure having a displacement along the two
directions (x and y) is said to be a global coordinates.
Write the element flexibility matrix for a beam element.
The element flexibility matrix (f) for a beam element is given by,
FAILURE ANALYSIS AND REHABILITATION OF STRUCTURES
UNIT β 1
Define Maintenance.
Maintenance is the act of keeping something in good condition by checking or repairing it regularly.
Define Repair.
Repair is the process of restoring something that is damaged or deteriorated or broken, to good condition.
Define Rehabilitation.
Rehabilitation is the process of returning a building or an area to its previous good conditions.
What are the two facets of maintenance?
The two facets of maintenance are,
Γ Prevention
Γ Repair
What are the causes of deterioration?
Γ Deterioration due to corrosion
Γ Environmental effects
Γ Poor quality material used
Γ Quality of supervision
Γ Design and construction flaws
How will you assess the deterioration?
Γ Visual inspection
Γ Study of available documentation
Γ Estimation of actual loads and environment effects
Γ Diagnosis
Define physical inspection of damaged structure.
Some of the useful information may be obtained from the physical inspection of damaged structure, like nature of distress, type of distress, extent damage and its classification etc. Their causes preparing and documenting the damages, collecting the samples for laboratory testing and analysis, planning for in situ testing, special environmental effects which have not been considered at the design stage and information on the loads acting on the existing structure at the time of damage may be, obtained. To stop further damages, preventive measure necessary may be planned which may warrent urgent execution.
How deterioration occurs due to corrosion?
Γ Spalling of concrete cover
Γ Cracks parallel to the reinforcement
Γ Spalling at edges
Γ Swelling of concrete
Γ Dislocation
Γ Internal cracking and reduction in area of steel reinforcement
What are the steps in selecting a repair procedure?
Γ Consider total cost
Γ Do repair job in time
Γ If defects are few & isolated repair on an individual basis. Otherwise do in generalized manner
Γ Ensure the repair prevents further development of defects
Γ In case of lost strength, repairs should restore the strength
Γ If appearance is a problem, the number of applicable types of repairs become limited & the repairs must be covered
Γ Repair works should not interface with facilities of the structure
Γ Take care in addition of section to a member and in redistributing live loads and other live load moments. After selecting a suitable method of repairs, and after considering all the ramifications of its application, the last step is to prepare plans & specification and proceed with the work.
Discuss about the environment effects which leads to deterioration of concrete structure.
Micro-cracks present in the concrete are the sources of ingress of moistures, atmospheric carbon di-oxide into the concrete which attack reinforcement and with various ingredients of concrete. In aggressive environment concrete structure will be severely reduces.
What is the effect of selecting poor quality material for construction?
Quality of materials, to be used in construction, should be ensured by means various tests as specified in the IS codes. Alkali-aggregate reaction and sulphate attack results in early deterioration. Clayey materials in the fine aggregates weaken the mortar aggregate bond and reduce the strength. Salinity causes corrosion of reinforcing bars as well as deterioration of concrete.
How can we determine the cause for deterioration of concrete structure?
Γ Inspect & observe the structure
Γ Observe in bad & good weather
Γ Compare with other constructions on the area or elsewhere & be patient
Γ Study the problem & allow enough time to do the job
What are the factors to be considered by the designer at the construction site?
Γ Minimum & maximum temperatures
Γ Temperature cycles
Γ Exposure to ultra violet radiation
Γ Amount of moisture
Γ Wet/dry cycles
Γ Presence of aggressive chemicals
What are the steps in repair aspect?
Γ Finding the deterioration
Γ Determining the cause
Γ Evaluating the strength of existing building or structure
Γ Evaluating the need of repair
Γ Selecting & implementing a repair procedure
Define the fixed percentage method of evaluating the strength of existing structure.
It is to assume that all members which have lost less than some predetermined % of their strength are still adequate and that all members
which have lost more than the strength are inadequate. It is usually from 15% onwards higher values are applicable for piling & stiffness bearing plates etc.
Discuss about the design and construction errors leading to deterioration of a structure.
Design of concrete structures governs the performance of concrete structures. Well designed and detailed concrete structure will show less deterioration in comparison with poorly designed and detailed concrete, in the similar condition. The beam-column joints are particularly prone to defective concrete, if detailing and placing of reinforcement is not done properly. Inadequate concrete cover may lead to carbonation depth reaching up to the reinforcement, thus, increasing the risk of corrosion of the reinforcement.
Discuss about the quality of supervision to be followed at a site.
Construction work should be carried out as per the laid down specification. Adherence to specified water-cement ratio controls strength, permeability, durability of concrete. Insufficient vibration may result in porous and honey combined concrete, whereas excess vibration may cause segregation.
What are the possible decisions that can be made after evaluating the strength of a structure?
Γ To permit deterioration to continue
Γ To make measures to preserve the structure in its present condition without strengthening
Γ To strengthen the construction
Γ If deterioration is exceptionally severe, to reconstruct or possibly abandon it
How can we evaluate the strength of existing structure by stress analysis?
This method is to make detailed stress analysis of the structure, as it stands including allowances for loss of section where it has occurred. This is more difficult & expensive. Here also the first step is to make preliminary analysis by fixed percentage method and if it appears that major repairs will be required, the strength is reevaluated based on detailed stress analysis, considering all contributions to such strength.
Define the load test method of evaluating the strength of existing structure.
Load tests may be required by the local building offered, but they should only be performed where computation indicated that there is reasonable margin of safety against collapse. Load test show strengths much greater than computed strengths when performed on actual structures. In repair work every little bit of strength is important.
What are the possible decisions after finding a structure to be inadequate?
Γ If the appearance of the existing condition is objectionable β repair now
Γ If appearance is not a problem then put the condition under observation to check if it is dormant or progressive
Γ If dormant β no repair
Γ If progressive β check the feasibility & relative economics of permitting deterioration to continue and performing a repair at some later date & of making the repair right away
What are the objectives of condition assessment?
The main purpose of guide is to briefly describe how to carry out the condition assessment of buildings before taking up repair and upgrading work. This will determine whether or not a distressed building should be demolished to build back better or whether it will be cost effective to either repair or retrofit it, in the context of overall safety.
What are the factors causing building distress?
Γ The reason for distress during service is the lack of maintenance of the building which results in deterioration / aging of materials and structural components leading to corrosion and cracking
Γ Buildings or structures are damaged at different grades of damage when they experience extreme loading conditions like in severe earthquakes or cyclonic storms for which they are not designed
Γ They may also fail if the building including the foundation is not properly designed and constructed following the standard codes of practice
Γ Inadequacy of design and poor quality of construction and maintenance are therefore the main reasons for the distress seen in buildings during service or under natural hazards
Explain the term crazing.
Crazing is the development of a network of fine random cracks on the surface of concrete or mortar caused by shrinkage and is usually related to finishing and curing procedures.
UNIT β 2
How can you prevent the effect of freezing and thawing in concrete?
Concrete can be restricted from frost action, damage of the structure by the entrainment of air. This entrainment of air is distributed through the cement paste with spacing between bubbles of no more than about 0.4mm.
Write any two tests for assessment of frost damage?
The frost damage can be assessed by several ways:
Γ Assessment of loss of weight of a sample of concrete subjected to a certain number of cycles of freezing and thawing is one of the methods
Γ Measuring the change in the ultrasonic pulse velocity or the damage in the change in the dynamic modulus of elasticity of specimen is another method
How does a concrete structure get affected by heat?
Heat may affect concrete and as a result of:
Γ The removal of evaporable water
Γ The removal of combined water
Γ Alteration of cement paste
Γ Alteration of aggregate
Γ Change of the bond between aggregate and paste
How can you control cracks in a structure?
Γ Use of good coarse aggregates free from clay lumps
Γ Use of fine aggregate free from silt, mud & organic constituent
Γ Use of sound cement
Γ Provision of expansion & contraction joint
Γ Provide less water-cement ratio
Define aggregate splitting?
This phenomenon occurs most frequently when hard aggregates are used in concrete. The thermal stresses except close to corners are predominantly compressive near to the heated surface. This stress causes the aggregate to split in this direction and the fractures may propagate through the mortar matrix leading to deterioration.
What are the various chemical attacks of concrete?
Γ Acid attack
Γ Alkali attack
Γ Carbonation
Γ Chloride attack
Γ Leaching
Γ Salt attack
Γ Sulphate attack
What are the factors affecting chemical attack on concrete?
Γ High porosity
Γ Improper choice of cement type for the conditions of exposure
Γ Inadequate curing prior to exposure
Γ Exposure to alternate cycles of wetting and drying
Write the methods of corrosion protection?
Γ Corrosion inhibitors
Γ Corrosion resisting steels
Γ Coatings for steel
Γ Cathodic protection
List out the methods to protect steel from corrosion.
Γ Coating to reinforcement
Γ Galvanized reinforcement
Γ Improving metallurgically by addition of certain elements
Γ Using stainless steel
Γ Using non β ferrous reinforcement
Γ Using corrosion inhibitors
Γ Coating to concrete
Γ Cathodic protection, either by means of impressed unit or by sacrificial anodes
Γ Electrochemical chloride removal
Γ Improving the cover concrete
List out some coating for reinforcement to prevent corrosion.
Γ Organic coating
Γ Epoxy coating
Γ Metallic coating
Γ Zinc coating
Define corner reparation?
This is a very common occurrence and appears to be due to a component of tensile stress causing splitting across a corner. In fire tests, corner separation occurs most often in beams and columns made of Quartz aggregate and only infrequently with light weight aggregates
List any four causes of cracks?
Γ Use of unsound material
Γ Poor & bad workmanship
Γ Use of high water-cement ratio
Γ Freezing & thawing
Γ Thermal effects
Γ Shrinkage stresses
What are the types of cracks?
Γ Class-1: Cracks leading to structural failure
Γ Class-2: Cracks causing corrosion
Γ Class-3: Cracks affecting function
Γ Class-4: Cracks affecting appearance
What are alkali aggregate reaction cracks?
Alkali aggregate reactivity is a type of concrete deterioration that occurs when the active mineral constituents of some aggregates react with the alkali hydroxides in the concrete. Alkali aggregate reactivity occurs in two forms such as Alkali Silica Reaction (ASR) and Alkali Carbonate Reaction (ACR). Indications of the presence of alkali aggregate reactivity
may be a network of cracks, closed or spalling joints, or displacement of different portions of a structure.
What changes occur, when hot rolled steel is heated to 500oc?
At temp of 500oc-600oc the yield stress is reduced to the order of the working stress and the elastic modulus is reduced by one-third. Bars heated to this temp virtually recover their normal temperature.
List out the various types of spalling?
Γ General or destructive spalling
Γ Local spalling which is subdivided as
Β· Aggregate splitting
Β· Corner separations
Β· Surface spalling
Β· Sloughing off
List some faults in construction planning?
Γ Overloading of members by construction loads
Γ Loading of partially constructed members
Γ Differential shrinkage between sections of construction
Γ Omission of designed movement joints
Define corrosion?
The gradual deterioration of concrete by chemically aggressive agent is called βCorrosionβ.
Give some examples for corrosion inhibitors?
Γ Anodic inhibitors
Γ Cathodic inhibitors
Γ Mixed inhibitors
Γ Dangerous & safe inhibitors
Define effective cover?
The cover to reinforcement measured from centre of the main reinforcement up to the surface of concrete in tension is called βEffective coverβ.
Define corrosion inhibitor?
Corrosion inhibitor is an admixture that is used in concrete to prevent the metal embedded in concrete from corroding.
What are the operations in quality assurance system?
Γ Feedback
Γ Auditing
Γ Review line
Γ Organization
List the various components of quality control.
Five components of a quality (control) assurance system are:
Γ Standards
Γ Production control
Γ Compliance control
Γ Task and responsibilities and
Γ Guarantees for users
UNIT β 3
What is expansive cement?
A slight change in volume on drying is known as expansion with time will prove to be advantage for grouting purpose. This type of cement which suffers no overall change in volume on drying is known as βExpansive cementβ.
What is the action of shrink comb in expansive cement?
Shrink comb grout acts like a Portland cement. It (shrinks) sets and hardens; it develops a compressive strength of about 140kg/cm2 at 7days and 210kg/cm2 at 28 days.
List the various types of polymer concrete.
Γ Polymer impregnated concrete (PIC)
Γ Polymer cement concrete (PCC)
Γ Polymer Concrete (PC)
Γ Partially impregnated & surface coat
Give the various monomers used in polymer concrete.
Γ Mehylmethacrylate (MINS)
Γ Styretoc
Γ Aerylonitrile
Γ t-butyle slynene
Define polymer concrete.
Polymer concrete is an aggregate bound polymer binder instead of Portland cement as in conventional concrete polymer concrete is normally use to minimize voids volume in aggregate mass. This can be achieve by properly grading and mixing of aggregate to attain the maximum density and the aggregates to attain minimum void volume. The entrapped aggregates are prepacked and vibrated in a mould.
What are the uses of Polymer concrete?
During curing Portland cement form mineral voids. Water can be entrapped in these voids which are freezing can readily attack the concrete. Also alkaline Portland cement is easily attached by chemically aggressive materials which results in rapid determination, there as using polymers can compact chemical attack.
What is sulphur infiltrated concrete?
New types of composition have been produced by the recently developed techniques of impregnating porous material like concrete with sulphur. Sulphur impregnation has shown great improvement in strength.
What are the applications of sulphur infiltrated concrete?
Sulphur β (impregnated) infiltration can be employed in the precast industries. Sulphur infiltration concrete should found considerable use in industry situation where high corrosion resistant concrete is required. This method cannot be conveniently applied to cast- in place concrete Sulphur impregnation has shown area improvement in strength.
What is drying shrinkage?
Concrete made with ordinary Portland cement shrinks while setting due to loss of water concrete also shrinks continuously for long time. This is known as βdrying shrinkageβ.
What is Self β Stressing cement?
This cement when used in concrete with restrained expansion includes compressive stresses which approximately offset the tensile stresses induced by shrinkage is known as βSelf-Stressing cementβ
What is polymer impregnated concrete?
PIC is a widely used polymer composition concrete, cured and dried in over or dielectric heating from which the air in the (pipes) open cell is removed by vacuum. Then low density manpower is diffused through an open cell and polymerized by using radiation, application of heat or by chemical initiation.
Define polymer partially impregnated concrete.
Polymer partially impregnated or coated in dep (CID) and surface coated (SC) control partially polymer impregnated concrete is used to increase the strength of concrete. Partially impregnated concrete is sufficient in situations there the major required surface persistent against chemical and mechanical attacks.
How can we manufacture sulphur infiltrated concrete?
Sulphur is heated to bring it into molten condition to which coarse and fine aggregates are poured and mixed together. On cooling, this mixture gave fairly good strength, exhibited acid resistance and also other chemical resistance, but it proved to be either than ordinary cement concrete.
What is the difference between ordinary cement and expansive cement?
Ordinary concrete shrinks while setting whereas expansive cement expands while setting.
What are the uses of gas forming and expansive chemicals?
Gas formation and expansive chemicals to produce light weight concrete as well as to cause expansion on application such as grouts for anchor bolts. They are non-striking type. Principal chemicals used are Hydrogen peroxide, metallic aluminium or activated carbon. Sometimes bentonite clays and natural gum are also used.
What is the use of corrosion inhibiting chemicals?
They resist corrosion of reinforcement in adverse environment sodium benzonate, calcium lingo sulphonate and sodium nitrate have good results.
Write the use of antifungus admixtures.
These are added to control and inhibit growth of bacteria or fungus in surfaces expressed t moisture. Polyhalogenated phenol, Dieldrin emulsion and copper compounds are some of the chemicals used for this.
What are the uses of curing compounds?
They are either wax based or resin based. When coated in freshly laid concrete they form a temporary film over the damp surface which stops water evaporation and allows sufficient moisture retention in concrete for curing.
Define sealants.
Sealants are flexibilized polymeric materials which are used for two purposes. They are,
Γ To plug irregular gap between two rigid surfaces
Γ To provide a dynamic bridge across the gap between two surfaces
What are the uses of sealants?
They are used to seal designed joints. They are formulated from synthetic rubbers or polysulphides. The choice of a sealant depends on the location of the joint, its movement capability and the function of the sealant is expected to perform.
What are the uses of flooring?
These are usually toppings based on metallic or non-metallic aggregates which are mixed with cement and placed over freshly laid concrete sub floor. These compounds in high viscosity liquid, form mixed with recommended filters at site, are based on resins and polymers such as epoxy, acrylic, polyurethane or polysulphide.
UNIT β 4
What is Vacuum concrete?
Only about half of the water added in concrete goes into chemical combination and the remaining water is used to make concrete workable. After laying concrete, water which was making concreting workable is extracted by a special method known as βvacuum methodβ.
What are the equipments used in vacuum concrete?
The equipment essentially consists of:
Γ Vacuum pump
Γ Water separator
Γ Filtering mat
What is Gunite?
Gunite can be defined as mortar conveyed through a hose and pneumatically projected at a high velocity on to a surface.
What are the two types of process in shotcrete?
Γ Wet mix process
Γ Dry mix process
What are the stages in dry mix process in shotcrete?
Γ In this process, the concrete is mixed with water as for ordinary concrete before conveying through the delivery pipeline to the nozzle, at which point it is jetted by compressed air, onto the work in the same way as that if mix process.
Γ The wet process has been generally desired in favour of the dry mix process, owing to the greater success of the latter.
What is shotcrete?
Shotcrete is a recent development on the similar principle of guniting for achieving greater thickness with small coarse aggregate.
What are the preliminary investigations before demolition of a structure?
The demolition contractor should have ample experience of the type of work to be offered
Γ Fully comprehensive insurance against all risks must be maintained at all times
Γ An experienced supervisor should be continuously in charge of the work
Γ The contract price should include all safety precautions included in the relevant building regulations
Γ The completion date should be realistic, avoiding and need to take risks to achieve the date
Write about protective clothing given before demolition.
Buildings where chemicals have been stored or where asbestos, lead paint, dust or fumes may be present will require specialized protective clothing.
Give a brief note on shoring and underpinning in demolition.
The demolition contractor has a legal obligation to show technical competence when carrying out the work. When removing sections of the building which could have leave other parts unsafe, adequate temporary supports and shoring etc. must be provided.
What are the major factors in selecting a demolition procedure?
Major factors to be considered in selecting an appropriate technique include:
Γ Safety of personnel and public
Γ Working methods
Γ Legislation applicable
Γ Insurance cover
Give the categories of demolition techniques.
Demolition techniques may be categorized as:
Γ Piecemeal demolition, using hand-held tools or machines, to reduce the height of the building or structure gradually
Γ Deliberate controlled collapse, demolition to be completed at ground level
Write short notes on demolition by hand.
Demolition of buildings or structure by hand-held tools such as electric or pneumatic breakers, sometimes as a preliminary to using other methods, should be carried out, where practicable, in the reverse order to the original construction sequence. Lifting appliances may be necessary to hold
larger structural members during cutting and for lowering severed structural members and other debris.
In what cases demolition by machine can be done?
Simple roof structures supported on wall plates should normally be demolished to the level of wall plates by hand, but if this may involve unsafe working, then demolition totally by machine may be appropriate.
Write short notes on balling machine.
Balling machines generally comprise a drag-line type crawler chassis fitted with a lattice crane jib. The demolition ball, with a steel anti-spin device, is suspended from the lifting rope and swung by the drag rope.
How are explosives used for demolition of a structure?
If explosives are to be used for demolition, the planning and execution, include pre-weakening, should be under the control of a person competent in these techniques. For large demolition, the competent person is likely to be an experienced explosive engineer; for smaller work, a shot-firer may be sufficient.
What is a hydraulic pusher arm?
Articulated, hydraulically-powered pusher-arm machines are normally mounted on a tracked or wheeled chassis, and have a toothed plate or hook for applying a horizontal force to a wall. The machine should stand on a firm level base and apply force by a controlled movement of the pusher arm.
What is pre-weakening?
Buildings and structures normally have structural elements designed to carry safely the loading likely to be imposed during their life.
As a preliminary to a deliberate controlled collapse, after loads such as furnishings, plant and machinery have been removed, the demolition contractor may be able to weaken some structural elements and remove those new redundant. This pre – weakening is essentially a planned exercise and must be preceded by an analysis of its possible effects on the structure until it collapses, to ensure that the structural integrity of the building is not geopardized accidentally. Insufficient information and planning relating to the structure may result in dangerous and unsafe work.
What is deliberate collapse?
The deliberate collapse of the whole or part of a building or structure requires particularly high standards of planning, supervisions and execution, and careful consideration of its effect on other parts of the structure or on adjacent buildings or structures. A surrounding clear area and exclusion zone are required to protect both personnel and property from the fall of the structure itself and debris which may be thrown up by the impact.
How can you develop a demolition strategy?
The strategy will need to take into account the method of construction used for the original building and its proximity to other buildings, structures and the general public. These factors, together with location, the cost and availability of tipping and disposal and the desirability and economics of
reuse, must be taken into account in the development of an appropriate strategy for the demolition of a structure.
What are nibblers?
Nibblers use a rotating action to snap brittle materials such as concrete or masonry. In either case, material should be removed from the top of walls or columns in courses not greater than 600mm in depth, steel reinforcement should be cut separately as necessary.
What are the considerations before demolition?
Considerations should be given to:
Γ Conducting a site and building survey, with a structural basis
Γ The examination of drawings and details of existing construction where available
Γ The preparation of details and drawings from site survey activities where no such information is available
Γ Establishing previous use of premises, especially with regard to flammable substances or substances hazardous to health or safety
Γ Programming the sequence of demolition work
Γ The preparation of a Method Statement.
UNIT β 5
Define stitching.
The tensile strength of a cracked concrete section can be restored by stitching in a manner similar to sewing cloth.
What do you mean by blanketing?
This is the simplest and most common technique for sealing cracks and is applicable for sealing both fine pattern cracks and larger isolated. The cracks should be dormant unless they are opened up enough to put in a substantial pattern in which case the repair may be more properly termed as βBlanketingβ.
Define external stressing.
Development of cracking in concrete is due to tensile stress and can be arrested by removing these stresses. Further the cracks can be closed by including a compressive force sufficient to overcome the tension and residual compression.
Write short notes on Autogenous healing.
The inherent ability of concrete to heal cracks within βautogenous healingβ. This is used for sealing dormant cracks such as precast units cracked in handling of cracks developed during the precast pilling sealing of cracks in water hands and sealing of cracks results of temporary conditions.
What is overlay?
Overlays may be used to restore a spelling or disintegrated surface or to protect the existing concrete from the attack of aggressive agents. Overlays used for this purpose include concrete or mortar, bituminous compounds etc. Epoxies should be used to bond the overlays to the existing concrete surface.
Give short note on Jacketing.
Jacketing consists of restoring or increasing the section of an existing member by encasing it in a new concrete. This method is useful for protection of section against further deterioration by providing additional to in member.
Give an account on how metal bonding is done on concrete member.
On the tension side of the beam 2to 3mm steel plates are to the existing beam to increase its capacity. The glue or adhesive should compatible with the existing concrete with behavioral characteristics under load addition to providing integrity with parent member.
How clamps are used to overcome low member strength?
The distress is due to inadequate stirrups either due to deficiency in the provision of C- stamps, U-clamp fixed externally along the length of beam to provide adequate these will be protected by covering with rich mortar or concreting as the a later stage.
Define grouting.
Grouting can be performed in a similar manner as the injection of an epoxy. However the use of an epoxy is the better solution except where considerations for the resistance of cold weather prevent such use in which case grouting is the comparable alternative.
Give a short note on epoxy coatings.
These are organic compound which when activated with suitable hardening agents form strong chemically resistant structures having excellent adhesive properties. They are used as binders or adhesives to bond new concrete patches to existing surfaces or hand together cracked portions. Once hardened, this compound will not melt, flow or bleed. Care should be taken to place the epoxy within the pot life period after mixing.
What are protective surface coatings?
During of concrete can be substantially improved by preventive maintenance in the form of weather proofing surface treatments. These treatments are used to seal the concrete surface and to inhibit the intrusion of moisture or chemicals.
List some materials used as protective surface coatings.
Materials used for this purpose include oils such as linseed oils, petroleum etc.
Define dry pack.
Dry packing is the hand placement of a very dry mortar and subsequent tamping or ramming of the mortar into place producing an intimate contact between the old and new concrete work.
Give a brief account on routing and sealing.
This method involves enlarging the cracks along its exposed surface, filling and finally sealing it with a suitable material. This is the simplest and most common technique for sealing cracks and is applicable for sealing both fine pattern cracks and larger isolated.
What is pneumatically applied mortar?
Pneumatically applied mortar is used for the restoration of when the location of deterioration is relatively at shallow depth. It can be used on vertical as well as on horizontal surfaces and is particularly restoring surfaces spalled to corrosion of the reinforcement. Damaged concrete elements also retrofitted using this method. This also has known as gunning or shotcreting techniques.
What is caging with steel?
A steel caging is prepared and made to surround the existing masonry so that lateral expansion when it is loaded in compression. The confinement of masonry will steel cage increases its capacity and ductility.
What are the techniques required for repairing cracks?
Γ Bonding with epoxies
Γ Routing and sealing
Γ Stitching
Γ Blanketing
Γ External stressing
Γ Grouting
Γ Autogenous healing
Give a brief note on dogs in stitching.
The dogs are thin and long and to cannot take much of compressive force. The dogs must be stiffened and strengthened by encasement in an overlay or some similar means.
Give some concrete materials used to overcome weathering action on concrete.
The two concrete repair materials used were,
Γ A flow able concrete with 16 mm aggregate and containing a plasticizer and a shrinkage-compensating additive, to be cast against forms in heights up to 1.5m, and
Γ A patching mortar to be applied by rendering, for areas less than .01m2
