# Beam problem - cross section

1. Oct 29, 2012

### pukb

Consider the cross section of two beams of same material as shown in the file attached.

The area moment of inertia I about the central axis is equal for both the c/s. I have calculated it.

Can somebody explain why the second c/s (2 in the figure ) is preferred for the design?

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2. Oct 29, 2012

### Studiot

Is this laminated timber?

Unless there is some structural connection between the leaves you have calculated the moment of inertia incorrectly for the second section.

3. Nov 1, 2012

### pukb

It is laminated timber.
To solve the problem, lets assume the laminaes are constrained at the ends to avoid their separation in bending.

4. Nov 1, 2012

### Studiot

You have to do more than constrain them at the ends.

At every vertical section along the beam there has to be a way to transfer the horizontal (shear) forces through the vertical section. Friction between the planks is not enough and indeterminate.

5. Nov 2, 2012

### pukb

We can probably assume a thin layer of adhesive between laminae to hold them together and transfer shear forces and no failure in the adhesive layers.
But still cant figure out why the second setup is preferred over the first.

6. Nov 2, 2012

### Studiot

So we have discussed the difference between a stack of planks and solid block.

I pointed out in post#2 that your calculation of moment of inertia was wrong.

If you glue the planks together to perform composite structural action then they will indeed have the same moment of inertia as a block of the same dimensions.

But so what?

They will have other properties that are very very different.

In particular timber is a significantly anisotropic material, so that it is particularly subject to twisting and warping under torques.

One advantage of glulam construction is that adjacent lpies have their grains running in different directions. The result of this is much greater dimensional stability and the resultant material is much closer to isotropy.

Is this what you are asking?

7. Nov 3, 2012

### Jupiter6

The 2nd cross section is preferable in that it would resist transverse shear the best?

8. Nov 3, 2012

### pukb

Studiot: post 6

The explanation seems to be sensible for a wooden beam. But why would somebody prefer the second cross section for say a metallic beam of aluminium or mild steel.

Jupiter :
Could you please explain how does it resist shear better?

Please highlight any problems that would occur if the second setup is used.