Civil Engineering - Theory of Structures - Discussion

19. 

The ratio of the length and depth of a simply supported rectangular beam which experiences maximum bending stress equal to tensile stress, due to same load at its mid span, is

[A].
[B].
[C].
[D].

Answer: Option B

Explanation:

No answer description available for this question.

Ranjit Ray said: (Dec 19, 2016)  
Mmax = wl/4.
Bending stress = M/z
Tensile stress = w/bd
z = bd2/6.
By solving & equating we will get the answer.

Chhaya said: (Apr 26, 2017)  
Thanks @Ranjit.

Sumit said: (Aug 20, 2017)  
Z is the moment of inertia or what?

Asay said: (Nov 21, 2017)  
Bending Stress=M(max)/Z
=(PL/4)/(I/y)
=(PL/4)/[(bd^3/12)/(d/2)]
=(PL/4)/[bd^2/6]
=3PL/2bd^2
Now,
Tensile Stress=P/A
=P/bd.

Since, according to question,
Bending Stress=Tensile Stress
PL/2bd^2=P/bd.
====> L/d=2/3

So, B is the correct Answer.

Snigdha said: (Feb 15, 2020)  
Thank you @Asay.

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