Bending of members made of several materials

[Dell]

when given a non homogeneous cross section, i know that i can find the bending(normal ) stresses by transforming the cross section into a homogeneous one by multiplying the area of one of the materials be 'n', where n=E1/E2,
then i solve normally, finding the centroid of the new cross section, finding the moment of inertia, and then simply using stress=-y*M/I, finally when calculationg the stress for the second material(the one i transformed), i multiply the answer i got by the same'n' i used.

can this method be used to calculate the shear stress somehow?? how would i find the shear stress in a non homogeneous cross section,

if stress=V*Q/(Ib) how do i calculate Q and I? can i use the same normal as in normal stress

 

[pongo38]

Exactly. That is how you do determine the stress needs of whatever is fastening the two materials together, be it glue, welds or some other discrete fastener such as rivets.

 

[Mene]

?

I can confirm that the method described in the content can be used to calculate the bending stresses for a non-homogeneous cross section. By transforming the cross section into a homogeneous one, the cross section can be treated as a single material with a uniform modulus of elasticity. This allows for the use of standard equations for calculating bending stresses.

However, this method cannot be directly applied to calculate shear stresses. Shear stresses are caused by forces parallel to the cross section, rather than perpendicular forces that cause bending stresses. To calculate shear stresses, the first step would be to determine the shear force and then use the equation stress=V*Q/(Ib), where Q is the first moment of area about the neutral axis and I is the moment of inertia. These values can be calculated using the same approach as for bending stresses, by finding the centroid and moment of inertia of the transformed cross section.

It is important to note that the value of n used for calculating bending stresses may not be the same as the value used for shear stresses. This is because the modulus of elasticity for a material can vary depending on the type of stress applied. Therefore, it is necessary to use the appropriate value of n for each type of stress.

In conclusion, while the method described in the content can be used to calculate bending stresses for non-homogeneous cross sections, a different approach is needed to calculate shear stresses. Both methods require the determination of the centroid and moment of inertia of the transformed cross section.