# Shear, Torsion, Bond, Anchorage and Development Length

 Question 1
M20 concrete as per IS 456: 2000 refers to concrete with a design mix having
 A an average cube strength of $20 \mathrm{MPa}$ B an average cylinder strength of $20 \mathrm{MPa}$ C a 5-percentile cube strength of $20 \mathrm{MPa}$ D a 5-percentile cylinder strength of $20 \mathrm{MPa}$
GATE CE 2023 SET-2   RCC Structures
Question 1 Explanation:
In M20, M refers to mix and 20 to characteristic cube strength. As per clause no. 6.1.1, IS456: 2000 characteristic strength is defined as the strength below which not more than 5 percent of the test results are expected to fall.
Hence, correct option is (C).
 Question 2
A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of $M30$ grade concrete. It has 1% longitudinal tension reinforcement of $Fe 415$ grade steel. The design shear strength for this beam is 0.66 $N/mm^2$. The beam has to resist a factored shear force of 440 kN. The spacing of two-legged, 10 mm diameter vertical stirrups of $Fe 415$ grade steel is ______mm. (round off to the nearest integer)
 A 127 B 101 C 254 D 331
GATE CE 2022 SET-1   RCC Structures
Question 2 Explanation:
$b=300mm$
$d=580 mm$
$V_u=440 kN$
Concrete used is M30
Raft steel is Fe415
$V_{cu}=\tau _c Bd=0.66 \times 300 \times \frac{580}{1000}=114.84 kN$
$V_{su}=V_u-V_{cu}=440-114.84=325.16 kN$
Spacing of 2-legged shear reinforcement
\begin{aligned} s_V&=\frac{A_{SV} \times 0.87 f_y \times d}{V_{su}}\\ &=\frac{2 \times \frac{\pi}{2} \times (10)^2 \times 0.87 \times 415 \times 580}{325.16 \times 1000}\\ &=101.16 mm \end{aligned}

 Question 3
A reinforcing steel bar, partially embedded in concrete, is subjected to a tensile force P. The figure that appropriately represents the distribution of the magnitude of bond stress (represented as hatched region), along the embedded length of the bar, is A A B B C C D D
GATE CE 2020 SET-1   RCC Structures
 Question 4
Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and concrete is 2 MPa, and the joint gap between the slabs is 10 mm. Ignoring the loss of bond and the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer) is _____
 A 350 B 700 C 1050 D 850
GATE CE 2019 SET-1   RCC Structures
Question 4 Explanation: $L_d=\frac{\phi \sigma _{st}}{4\tau _{bd}}=\frac{12 \times 230}{4 \times 2}=345mm$
Length of tie bar $=L_d+10+L_d=345+10+345=700mm$
 Question 5
For a given loading on a rectangular plain concrete beam with an overall depth of 500 mm, the compressive strain and tensile strain developed at the extreme fibers are of the same magnitude of $2.5 \times 10^{-4}$. The curvature in the beam cross-section (in $m^{-1}$, round off to 3 decimal places), is ____
 A 0.008 B 0.006 C 0.004 D 0.001
GATE CE 2019 SET-1   RCC Structures
Question 5 Explanation:
Simple bending equation
\begin{aligned} \frac{m}{I}&=\frac{f}{y}=\frac{E}{R} \\ \frac{1}{R}&=\frac{f}{E}\cdot \frac{1}{y} \\ &=\frac{\varepsilon }{y}=\frac{2.5 \times 10^{-4}}{(0.5/2)}=0.001m^{-1} \end{aligned}

There are 5 questions to complete.