Civil Engineering - Theory of Structures - Discussion

14. 

Keeping the depth d constant, the width of a cantilever of length l of uniform strength loaded with a uniformly distributed load w varies from zero at the free end and

[A]. at the fixed end
[B]. at the fixed end
[C]. at the fixed end
[D]. at the fixed end

Answer: Option C

Explanation:

No answer description available for this question.

Anshul Gupta said: (Sep 25, 2013)  
Sigma denoted by S.

And Z(section modulus) = bd2/6.

Then,

B.M. at fixed support is wl2/2.

wl2/2 = S*Z.

wl2/2 = S*bd2/6.

b= (3wl2)/Sd2.

Answer C.

Nishant Jain said: (Oct 16, 2016)  
Thanks @Anshul Gupta.

Mukesh Pal said: (Nov 4, 2016)  
Thank you @Anshul Gupta.

Ravi said: (Nov 18, 2016)  
This is not uniform load so b.m is not (w*l^2)/2 varying load so b.m is (w*i^2)/6 answer.

Akash said: (Jan 14, 2017)  
Yes, you are correct @Ravi.

Patil said: (Mar 30, 2017)  
Yes, @Ravi

You are correct, bm not wl^2/2. It is wl^2 /6 n final and is wl^2/(d^2*s).

Vijay Kumar said: (May 29, 2017)  
None of the above answers is correct. The Answer will be wl2/sd2.

Jeet Beniwal said: (Sep 21, 2017)  
You are wrong @Ravi.

Load is udl.
Width is o at free end.
And asked the width at fix end.

Lekhs said: (Dec 22, 2017)  
What is the right answer? Please explain me.

Chandan said: (Apr 28, 2018)  
Thanks @Anshul.

Dileep Pawaar said: (May 19, 2018)  
You are correct @Anshul Gupta.

Narayan said: (Oct 23, 2018)  
s= σ(direct stress).

M= wl^2-1/2*(l*w)*2/3(l)
= wl^2/6.

But,
M=S * Z.
wl^2/6 = S * b * d^2/6.
b = wl^2/s * d^2.

Nilraj. said: (Nov 20, 2018)  
@Ravi.

This is uniformly Distributed load.

Dhananjay said: (Feb 23, 2019)  
@Anshul,

How can you equate BM with S*Z? Here, units are different. Please explain.

Syed Mazhar said: (Dec 12, 2019)  
@Dhananjay.
From bending eq
M/I= f/y=E/R
M=(I/y)f
M=zf.

Shubham Siddharth Nayak said: (Nov 19, 2020)  
Cantilever carrying UDL- BM at fixed end = wl^2 /2.
We know, M = fz.
Wl^2/2= f *(bd^2/6),
b =3wl^2/fd^2.

Michael said: (Apr 19, 2021)  
Thanks @Anshul Gupta.

Bishwo said: (May 28, 2021)  
Bending moment at fixed =1/3 (wl^2) /2.

1/3 is because it's a triangular slab of thickness d and with b. 1 part of whole rectangle will give BM at the fixed end.

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