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
The deformation in concrete due to sustained loading is
A
creep
B
hydration
C
segregation
D
shrinkage
GATE CE 2018 SET-1   RCC Structures
Question 10 Explanation: 
Creep is inelastic deformation with time due to sustained loading
There are 10 questions to complete.

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