Mechanical Engineering - Strength of Materials - Discussion

First of all, It's Elastic Strength not Elastic modulus! Some guys using PL/AE formula for explaining this which is completely illogical. After that, Elastic strength means section modulus, which ultimately describes the load distributing and carrying capacity of beam throughout it's volume. Now when width and depth is considered then it can directly be observed by formula Z= bd'/6. But when length is considered then we have to observe the beam condition by providing a point load.

Now suppose a cantilever beam is there with with a point load, P at its free end. Now in first case if length is L then moment distribution will take place as, PL but when length is doubled then moment distribution will take place as 2PL, which ultimately lowers the strength of beam by fraction of 2. So elastic strength becomes half i.e. 1/2.

You can even imagine this, that same load P is producing double moment in second case that means beam strength will decrease.

Thankyou!

Elastic strength of the beam doesn't depend upon the length of the beam, so the answer is 'A'. More length is more elastic deflection only.

I think A is the right answer as the elastic strength of the beam depends upon the section properties not on span (section modules define elastic strength very well i.e. bd^2/6) so elastic strength will be the same in both cases.

Can anyone explain this?

Strength is proportional to section modulus.
Section modulus is inversely proportional to maximum bending stress.
The bending stress developed in beam B is twice that of beam A (using the bending equation).
So, the strength of beam B is half that of beam A.

Z = I/Ymax.
Za = bd^3/(12*d/2),
Zb = b(2d)^3/(12*2d/2),
ZaZb = 1/4.

σ = E * Strain;

We know that.
Strain=Change in length/Original length.
σ= E* Change in length/Original length.
When Original will be doubled elastic strength will be half.

One half,(b=a/2).
Pl/ae=2pl/ae.
A=2B.
B=A/2.

Option A is correct.

Strength doesn't depend on the length of the beam.
The strength of beam purely depends on its section modulus (Z).

So the correct answer is A.