Civil Engineering - Strength of Materials - Discussion

2. 

As compared to uniaxial tension or compression, the strain energy stored in bending is only

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

Answer: Option C

Explanation:

No answer description available for this question.

Samrat said: (Oct 11, 2014)  
How it is calculated?

Dipankar said: (Oct 29, 2014)  
Due to middle-third rule.

Subinsekhar said: (Nov 3, 2014)  
Can you explain?

Syed Aasif said: (Feb 25, 2015)  
We know strain energy stored is direct stress square/2.

Akash said: (Jul 9, 2015)  
Step 1: Calculate strain energy due to uniaxial loading.

Viz. U1 = {(f^2)xvol}/(2xE).

Step 2: Calculate strain energy due to pure bending.

Viz. U2 = 0.5xMxtheta.

= 0.5x[(fxI)/y]x[(Mxl)/(ExI)].

(from simple bending equation & moment area method resp.)

Solve it U2 = {(f^2)xvol}/(6xE).

i.e U2 = 0.3XU1.

:) :) :) :).

Subhra said: (Oct 9, 2015)  
@Akash,

Please explain me what is l?

Binit said: (Nov 13, 2015)  
Need more explanation.

Dheeraj Hindu said: (Aug 9, 2016)  
We know that,
FOR COMPRESSIOM OR TENSIOIN.

Strain energy(SE) = (1/2) * force * deformation = 1/2) * P * PL/AE = P^2L/2AE.

FOR BENDING.

SE = (P^2L^3)/6AE.

So bending (SE)= (L^2)/3 tension(SE).

Naren said: (Jan 14, 2017)  
Here, [SE] FOR COMPRESSION OR TENSION IS.

= 1/2 * force * deformation.

And what about [SE] for BENDING.

@Dheeraj Hindu.
Could you please explain this one.

Srinivas said: (Feb 25, 2017)  
How it is calculated?

Please explain me.

Surya said: (Apr 5, 2017)  
Please give the explanation.

Hiralal Singha said: (Jun 13, 2017)  
Not getting this, Explain it please.

Deepak said: (Jul 22, 2017)  
How to solve this? please explain.

Maneesha.Puvvala said: (Aug 15, 2017)  
Can you give me a deep explanation?

R N Yadav said: (Sep 5, 2017)  
Please explain it clearly.

Ajay Munde said: (Oct 28, 2017)  
Not getting this. Please explain.

Shakil said: (Jan 7, 2018)  
Due to avail stress =σ2/2E.vol.

Due bending = Σ2/6E.vol.

Jeldi said: (Jan 29, 2018)  
U= (σ^2*v)/2E -----> (axial loading)

U=(σ^2*v)/6E -----> (bending)

So ans is (1/3)

For bending
U=Ʃ[ (M^2)/2E ] dx{hear integration frm 0 to L}
U=[ (M^2)/2E ]*Ʃ1dx
U=[ (M^2)/2E ]*L
Now M/I = E/R=σ/y
So M=σ*I/y
On simplifying
U=(σ^2*v)/6E

Shalu said: (Mar 6, 2018)  
Can't understand can you explain?

Shiney said: (Mar 30, 2018)  
Will you please explain it clearly?

Sarang Mote said: (Jan 21, 2019)  
But the strain energy if load multiplied by displacement, Then in case of bending, how do we derive the formula.

Pawan said: (Mar 21, 2019)  
U= (σ^2*v)/2E -----> (axial loading).

U=(σ^2*v)/6E -----> (bending).

So, answer is (1/3).

Abhishek Thakur said: (Jul 11, 2019)  
For(tension and compression):

Due to the stress-strain curve the strain energy;

Resilience = 1/2 * stress * strain.
And proof resilience= 1/2* stress * strain * volume is;
Strain = stress/modulus of elasticity.
Then PR=stress^2*volume/2E.

And for bending moment due to pure axial loading.
M=Wx.

Strain energy due to bending moment = integration of M^2*xdx/2E= integration of (Wx)^2dx/2E (limit 0toL).

Put the value of Moment M here and on solving u will get;
W^2 l^3/6E.

On solving both the value you will get;
1/3.

Fahad said: (Oct 7, 2020)  
Thanks @Abhishek Thakur.

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