# Civil Engineering - Theory of Structures - Discussion

Discussion Forum : Theory of Structures - Section 4 (Q.No. 19)

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

Discussion:

6 comments Page 1 of 1.
Priya said:
6 months ago

Why moment is taken as wl/4? Please explain to me.

Snigdha said:
4 years ago

Thank you @Asay.

Asay said:
6 years ago

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.

=(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.

(1)

Sumit said:
6 years ago

Z is the moment of inertia or what?

(1)

Chhaya said:
6 years ago

Thanks @Ranjit.

Ranjit ray said:
7 years ago

Mmax = wl/4.

Bending stress = M/z

Tensile stress = w/bd

z = bd2/6.

By solving & equating we will get the answer.

Bending stress = M/z

Tensile stress = w/bd

z = bd2/6.

By solving & equating we will get the answer.

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