# Design of RC Structures Questions and Answers – Rectangular Beams

This set of Design of RC Structures Multiple Choice Questions & Answers (MCQs) focuses on “Rectangular Beams”.

1. For a rectangular beam, the permissible stress of concrete and steel are 140MPa(t) and 5MPa(c) and modular ratio 11. What is the critical neutral axis depth factor(k)?
a) .38
b) .48
c) .58
d) .28

Explanation: k=1/(1+r/m) [r=t/c=140/5=28]
=1/(1+28/11)=.2824

2. For a rectangular beam of 300*600mm2, the permissible stress of concrete and steel are 140MPa(t) and 5MPa(c) and modular ratio 11. What is the depth of the neutral axis?
a) 170mm
b) 270mm
c) 370mm
d) 470mm

Explanation: k=1/(1+r/m) [r=t/c=140/5=28] =1/(1+28/11)=.2824;
n=kd=.2824*600mm=169.44mm.

3. What is the modular ratio of a concrete of M20 grade reinforced with Fe250 steel?
a) 11
b) 9
c) 13
d) 3

Explanation: According to codal provision, m=280/(3*Ϭcbc)
Ϭcbc is 7 for M 20 grade concrete; m=13.3333

4. What is the critical neutral axis depth factor for Fe250 reinforced M20 grade concrete?
a) .40
b) .50
c) .60
d) .70

Explanation: IS 456:200 gives critical neutral axis depth factor k= 1/(1+.0107 Ϭst) [Ϭst=140MPa]
=1/(1+ .0107*140)=.40

5. If the modular ratio and percentage of steel is known, the neutral axis factor can be determined.
a) False
b) True

Explanation: According to the codal provision the neutral axis factor is dependent on the modular ratio m and percentage of steel p.
k=[2mp+(mp)2]1/2-mp; this is the desired equation to determine the neutral axis factor.

6. What is the percentage of steel (p) for Fe250 reinforced M20 grade concrete?
a) .98
b) .48
c) .58
d) .39

Explanation: p=50m Ϭcbc2/ Ϭst(m Ϭcbcst)=.98 [m=13; Ϭcbc =7MPa; Ϭcbc=140MPa]

7. For a rectangular beam of 300*600mm2, the permissible stress of concrete and steel are 140MPa(t) and 5MPa(c) and modular ratio 11. What is the lever arm factor?
a) .81
b) .71
c) .91
d) .61

Explanation: According to codal provision,
k=1/(1+r/m) r=t/c=140/5=28]
=1/(1+28/11)=.2824
j=1-k/3=.9058=.91

8. For a rectangular beam of 300*600mm2, the permissible stress of concrete and steel are 140MPa(t) and 5MPa(c) and modular ratio 11. What is the depth of lever arm?
a) 346mm
b) 546mm
c) 646mm
d) 746mm

Explanation: According to codal provision,
k=1/(1+r/m) [r=t/c=140/5=28]
=1/(1+28/11)=.2824
j=1-k/3=.9058=.91
a=jd=.91*600=546mm

9. For a rectangular beam of 300*600mm2, the permissible stress of concrete and steel are 140MPa(t) and 5MPa(c) and modular ratio 11. What is the stress ratio?
a) 38
b) 28
c) 48
d) 58

Explanation: r=t/c=140/5=28

10. For a rectangular beam of 300*600mm2, the permissible stress of concrete and steel are 140MPa(t) and 5MPa(c) and modular ratio 11.What is the area of reinforcement if it is subjected to 20kNm moment?
a) 281.64mm2.
b) 211.64mm2.
c) 261.64mm2.
d) 221.64mm2.

Explanation: According to codal provision,
k=1/(1+r/m) [r=t/c=140/5=28] =1/(1+28/11)=.2824
j=1-k/3=.9058=.91
a=jd=.91*600=546mm
Area of steel is= M/t*a=261.64mm2.

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