Limit State Method MCQ Quiz - Objective Question with Answer for Limit State Method - Download Free PDF

Explanation:

As per IS 456: 2000, Table 5;

According to IS 456: 200, the Minimum cement content and maximum water-cement ratio based on exposure conditions for plain cement concrete and reinforced cement concrete are given below:

Explanation:

• When testing concrete specimens for compressive strength, the height-to-lateral dimension ratio (also known as slenderness ratio) plays a significant role in how the material behaves under load.

• Shorter, stubby specimens (low height-to-diameter ratio) experience greater lateral confinement due to friction at the loading platens.

• This confinement increases the apparent strength as it resists lateral expansion.

• As the height increases relative to the diameter, the confining effect reduces.

• This leads to a more uniform stress distribution but less lateral restraint, causing the measured compressive strength to drop.

• Slender specimens are more prone to column-like failure (buckling or instability) rather than pure crushing.

• This changes the failure behavior and reduces the load-carrying capacity under compression.

• The standard height-to-diameter ratio used in most concrete compressive tests is 2:1.

• Deviating significantly from this ratio (especially increasing it) may result in underestimating the actual compressive strength of the concrete.

Additional Information

• Compressive strength is the maximum load per unit area that concrete can bear without failure when subjected to axial compression.

• It is considered the most essential mechanical property of concrete, as concrete is primarily used to resist compression rather than tension.

• This property helps engineers design structural elements like columns, beams, slabs, and footings safely and economically.

• The standard test is conducted by casting cylindrical or cubical concrete specimens, typically 150 mm × 150 mm × 150 mm cubes or 150 mm diameter × 300 mm height cylinders.

• These are cured under controlled conditions (usually 28 days) before testing.

• The specimen is placed in a compression testing machine, and the load is applied until failure.

Explanation:

• According to Whitney’s stress block theory and IS 456, the depth of the neutral axis $x_{u, \text{max}}$ for a balanced section (where steel yields just as concrete reaches its ultimate strain) is limited to about 0.53 to 0.537 times the effective depth $d$.

• This ensures the maximum permissible depth of the stress block for safe design before concrete crushing dominates.

Additional Information

• Whitney simplified the actual nonlinear stress distribution in concrete to an equivalent rectangular block.

• The factor 0.53d is key in limiting the depth of compression zone in design calculations.

• It helps distinguish between under-reinforced, balanced, and over-reinforced sections in concrete beam design.

Explanation:

Following assumptions have been made in IS 456: 200 regarding maximum strain in compression members:

1. As per, Clause 38.1, the maximum compressive strain in concrete in bending compression is taken as 0.0035.

2. As per, clause 39.1, the maximum compressive strain in concrete in axial compression is taken as 0.002.

Important Points

The  maximum compressive strain at the highly compressed extreme fibre in concrete subjected to axial compression and bending and when there is no tension on the section shall be 0.0035 minus 0.75 times the strain at the least compressed extreme fibre.

Explanation:

As per IS 456 (2000), Table 16, For main reinforcement, up to 12 mm diameter bar for mild exposure the nominal cover may be reduced by 5 mm. 

Additional Information

Nominal Cover to Meet Durability Requirements:

Nominal Cover to Meet Fire Resistance:
The nominal cover is the design depth of concrete cover to all steel reinforcements.

It shall be not less than the diameter of the bar.

Minimum values of the nominal cover of normal-weight aggregate concrete to be provided to all reinforcement to meet the specified period of fire resistance shall be given in the table below 

The assumed value of standard deviation for initial calculations as per IS 456 – 2000 are given below in the table:

Given:

Moment due to Dead load (DL)= 50 kNm

Moment due to live load (LL) = 50 kNm

Moment due to Seismic load (EL) = 20 kNm

Computation:

Design bending moment is Maximum of the following

1) Mu considering moment due to dead load and live load

Mu = 1.5 (DL+LL) = 1.5 x (50+50) = 150 kN-m

2) Mu considering moment due to dead load and Seismic load

Mu = 1.5 (DL+EL) = 1.5 x (50+20) = 105 kN-m

3) Mu considering moment due to dead load, live load and seismic load together

Mu = 1.2 (DL+LL+EL) = 1.2 x (50+50+20) = 144 kN-m.

Concept:

IS 875 (part 2) - 1987: Indian Standard Codes provides conservatively imposed loads for building and structures.

IS 875 (part 1) - 1987: Indian Standard Codes provides design dead loads(Unit weights of building material and stored materials) for buildings and structures.

IS 875 (part 3) - 1987: Indian Standard Codes provides design wind loads for buildings and structures.

IS 875 (part 4) - 1987: Indian Standard Codes provides design snow loads for buildings and structures.

IS 875 (part 5) - 1987: Indian Standard Codes provides design special loads(load combinations) for buildings and structures.

Additional InformationIS 800:2007 - Code for practice for general construction in steel.

IS 456:2000 - Code of practice for plain and reinforced concrete.

IS 1343:2012 - Code of practice for prestressed concrete.

Concept:

Values of the factor of safety (partial) for load combination:

Where, DL = Dead load, LL = Live load WL = Wind load EL = Earthquake load

Calculation:

Given: Dead load (DL) = 20 KN and Live load (LL) = 12 kN

Partial factor of safety = 1.5 (DL + LL) = 1.5 (20 + 12) = 48 kN

Additional Information

Values of the factor of safety (partial) for load combination:

Concept:

The correct expression as per IS 456: 2000 to find Target mean strength is:

fcm = fck + (1.65 × σ)

fcm = Target mean strength

fck = Characteristic strength

σ = Standard deviation

1.65 is generally a risk factor

Calculations:

fck = 20 N/mm2

σ = 4.0 N/mm2

Target mean strength is:

fcm = fck + (1.65 × σ)

fcm = 20 + (1.65 × 4)

fcm = 26.6 N/mm2

Explanation:

Concrete in Sea-water (as per IS 456: 2000)

Concrete in sea-water or exposed directly along the sea-coast shall be at least M 20 Grade in the case of plain concrete and M 30 in case of reinforced concrete.

The use of slag or pozzolana cement is advantageous under such conditions.

Concept:

Modular ratio:

In the elastic theory for the reinforced concrete structure, concrete and reinforcing steel are converted into one material. This is done by using the modular ratio ‘m’.

It is the ratio of modulus of elasticity of steel and concrete.

\(\rm m = \frac{{{E_s}}}{{{E_c}}}\)

However, concrete has varying moduli, as it is not a perfectly elastic material.

Short term modulus of elasticity:

The short-term modulus of elasticity is given by

 \(\left( {{E_c} = 5000\sqrt {{f_{ck}}} } \right)\) 

Long term modulus of elasticity:

The long-term modulus of elasticity is considered to take into account the effect of creep and shrinkage.

The modular ratio is taken as

\(m = \frac{{280}}{{3 \times {\sigma _{cbc}}}}\)

where σcbc is permissible compressive stress in concrete in bending.

Calculation:

Grade of concrete = M30

Modular ratio ‘m’ (without considering creep effect)

 \(m = \frac{{{E_s}}}{{{E_c}}} = \frac{{2 \times {{10}^5}}}{{5000\sqrt {{f_{ck}}} }} =\frac{{2 \times {{10}^5}}}{{5000\sqrt {{30}} }}\) = 7.30

Explanation:

As per IS 456, Clause 8.2.4.1 Table 6

Important Points

According to IS 456: 200 Table 5, the minimum cement content and maximum water-cement ratio based on exposure conditions for plain cement concrete and reinforced cement concrete are given below:

Concepts:

The factor of safety against sliding is defined as the resisting forces (friction and passive forces) divided by the driving lateral force. 

As per IS Code 1904: 1986, the minimum allowable factor of safety against sliding for a cantilever retaining wall should be 1.50 when dead load, live load, earth pressure are considered together with  either seismic forces or wind forces.  

However, in above case, if effect of wind force or earthquake forces is not considered then factor of safety is taken as 1.75 against sliding.

Note:

The minimum allowable factor of safety against overturning shall be 1.50, when dead load, live load, earth pressure are considered together with either seismic forces or wind forces. 

However, in above case, if effect of wind force or earthquake forces is not considered then factor of safety is taken as 2 against overturning.

Explanation:

Modulus of elasticity of concrete:

It is the parameter that measures concrete's resistance to elastic deformation when stress is applied to it. As per IS 456: 2000, short term modulus of elasticity of concrete Ec is given by,

\({\rm{E_c}} = 5000\sqrt {{{\rm{f}}_{{\rm{ck}}}}} \)

Where fck is the characteristics strength of concrete. It means the modulus of elasticity in concrete is proportional to the compressive strength of concrete.

Actual measured values may differ by ± 20 percent from the values obtained from the above expression, \({\rm{E_c}} = 5000\sqrt {{{\rm{f}}_{{\rm{ck}}}}} \).

Long term elastic modulus of elasticity (EL) = \(\dfrac{{5000\sqrt {{{\rm{f}}_{{\rm{ck}}}}} }}{{1 + {\rm{\theta }}}}\)

Where, \({\rm{\theta }} = {\rm{Creep\;coefficient}} = \dfrac{{{\rm{Ultimate\;creep\;strain\;}}}}{{{\rm{Elastic\;strain}}}}\) and fck = characteristic compressive strength