# Working Stress and Limit State Method

 Question 1
The maximum applied load on a cylindrical concrete specimen of diameter 150 mm and length 300 mm tested as per the split tensile strength test guidelines of IS 5816 : 1999 is 157 kN. The split tensile strength (in MPa, round off to one decimal place) of the specimen is _______.
 A 1.4 B 2.2 C 4.2 D 6.4
GATE CE 2020 SET-2   RCC Structures
Question 1 Explanation: P = 157 kN
D = 150 mm
L = 300 mm
In split tensile strength test, split tensile
strength of concrete
\begin{aligned} f_{et}&=\frac{2P}{\pi DL}=\frac{2 \times 157000}{\pi \times 150 \times 300}\\ &=2.22 N/mm^2 \end{aligned}
 Question 2
As per IS 456:2000, the pH value of water for concrete mix shall NOT be less than
 A 4.5 B 5 C 5.5 D 6
GATE CE 2020 SET-2   RCC Structures
Question 2 Explanation:
1. Minimum pH value of water for concrete = 6.0
As per IS code provision no. 5.4.2, the pH value of water shall not less than 6.0.
 Question 3
During the process of hydration of cement, due to increase in Dicalcium Silicate ($C_2S$) content in cement clinker, the heat of hydration
 A increases B decreases C initially decreases and then increases D does not change
GATE CE 2020 SET-1   RCC Structures
Question 3 Explanation:
Due to increase in $C_2S$ heat of hydration decreases.
 Question 4
When aspecimen of M25 concrete is loaded to a stress level of 12.5 MPa, a strain of $500 \times 10^{-6}$ is recorded. If this load is allowed to stand for a long time, the strain increasesto $1000 \times 10^{-6}$. In accordance with the provisions of IS:456-2000, considering the long-term effects, the effective modulus of elasticity of the concrete (in MPa) is________
 A 12500 B 1250 C 50000 D 5000
GATE CE 2019 SET-2   RCC Structures
Question 4 Explanation:
Effective modulus of elastic
\begin{aligned} E_{ce}&=\frac{E_c}{1+\theta } \\ E_c&= 5000\sqrt{f_{ck}}\\ &= 5000\sqrt{25}\\ &=25000MPa \end{aligned}
Creep coefcient
\begin{aligned} \theta &=\frac{\text{creep strain}}{\text{elastic strain}} \\ &= \frac{\text{longterm strain - elastic strain}}{\text{elastic strain}}\\ &=\frac{(1000 \times 10^{-6})-(500 \times 10^{-6})}{(500 \times 10^{-6})}=1\\ \therefore \;\;E_{ce}&=\frac{25000}{1+1}=12500MPa \end{aligned}
 Question 5
In the context of provisions relating to durability of concrete, consider the following assertions:

Assertion (1): As per IS 456-2000, air entrainment to the extent of 3% to 6% is required for concrete exposed to marine environment.

Assertion (2): The equivalent alkali content (in terms of $Na_2O$ equivalent) for a cement containing 1% and 0.6% of $Na_2O$ and $K_2O$, respectively, is approximately 1.4% (rounded to 1 decimal place).

Which one of the following statements is CORRECT?
 A Assertion (1) is FALSE and Assertion (2) is TRUE B Assertion (1) is TRUE and Assertion (2) is FALSE C Both Assertion (1) and Assertion (2) are FALSE D Both Assertion (1) and Assertion (2) are TRUE
GATE CE 2019 SET-2   RCC Structures
Question 5 Explanation:
(1) As per clause 8.2.2.3 of IS 456-2000, entrained air percentage of 3 to 6% is required to resist freezing and thawing,
i.e. not for marine environment.
Hence, Assertion (1) is wrong
Equivalent alkali content is terms of $Na_2O$
$= [Na_2 O] + 0.685 [K_2 O]$
$= 1 + 0.685 \times 0.6 = 1.41 \%$
Hence, Assertion (2) is correct
 Question 6
The characteristic compressive strength of concrete required in a project is 25MPa and the standard deviation in the observed compressive strength expected at site is 4MPa. The average compressive strength of cubes tested at different water-cement (w/c) ratios using the same material as is used for the project is given in the table. The water-cement ratio (in percent, round off to the lower integer) to be used in the mix is _____
 A 40 B 36 C 46 D 52
GATE CE 2019 SET-2   RCC Structures
Question 6 Explanation:
Target mean strength
\begin{aligned} &=f_{ck}+1.65\sigma \\ &= 25+1.65 \times 4.0\\ &= 31.6 \end{aligned}
Water content required, $=50-\frac{50-45}{35-25}\times (31.6-25)=46.7\%$
say 46% (round off to the lower integer)
 Question 7
In the reinforced beam section shown in the figure, the nominal cover provided at the bottom of the beam as per IS 456-2000, is A 30 mm B 36 mm C 42 mm D 50 mm
GATE CE 2019 SET-1   RCC Structures
Question 7 Explanation:
Nominal cover = Effective cover $-\frac{\phi _m}{2}-\phi _{st}$
$=50-\frac{16}{2}-12=30mm$
Nominal cover is the distance from extreme concrete fbre to the surface of stirrup.
 Question 8
As per IS 456 : 2000, the minimum percentage of tension reinforcement (up to two decimal places) required in reinforced-concrete beams of rectangular cross-section (considering effective depth in the calculation of area) using Fe500 grade steel is ______
 A 0.06 B 0.17 C 0.25 D 0.8
GATE CE 2018 SET-2   RCC Structures
Question 8 Explanation:
Minimum percentage of steel (for Fe 500 )
$=\frac{85}{f_{y}} \%=\frac{85}{500} \%=0.17 \%$
 Question 9
The frequency distribution of the compressive strength of 20 concrete cube specimens is given in the table. If $\mu$ is the mean strength of the specimens and $\sigma$ is the standard deviation, the number of specimens (out of 20) with compressive strength less than $\mu -3\sigma$ is ______
 A 0 B 1 C 2 D 3
GATE CE 2018 SET-1   RCC Structures
Question 9 Explanation:
Average strength,
\begin{aligned} \mu &=\frac{(4 \times 23)+(2 \times 28)+(5 \times 22.5)+(5 \times 31)+(4 \times 29)}{20} \\ &=26.575 \mathrm{MPa} \\ \sigma &=\sqrt{\frac{\Sigma(\mu-f)^{2}}{n-1}} \\ &=\sqrt{\frac{\begin{array}{c} (26.575-23)^{2} \times 4+(26.575-28)^{2} \times 2\\ +(26.575-22.5)^{2} \times 5+(26.575-31)^{2} \\ \times 5+(26.575-29)^{2} \times 4 \end{array}}{(20-1)}} \\&=3.7 \end{aligned}
Now, $\mu-3 \sigma=26.575-3 \times 3.7=15.48$
Thus, no specimen is having compressive strength less than $\mu-3 \sigma.$
 Question 10
 A creep B hydration C segregation D shrinkage
GATE CE 2018 SET-1   RCC Structures
Question 10 Explanation:
1.  