Question

If we use an I beam vs a solid beam will the support reactions and the force in each member stay the same? Assuming each member has a cross-sectional area of 180 mm² and E=kN/mm²,  Why or why not?

Statically Indeterminate Truss 1: VD 40 kN 3.0 m 3.0 m 6.0 m The cross-sectional area of all members is equal to 180 mm E-205 kN/mm2

Answer 1

The question purely aims at the theory behind the force calculations. And it aims at student's knowledge about the aspects of force and stress.

Even if we use I beam or any other different cross section the forces in the members will remain unchanged.!

Go back to the diagram and see that to solve the forces we don't need the anything that depends on the cross section.!

In solving these we only need the external forces acting and the balancing forces and the length of the members only. We here solve this by applying different theories like varignons theorem , lamis theorem , etc to equate forces . And we are not using any cross sectional details in these.

The stress in the members depends on area of section (when it is a direct stress which can be tensile , compressive or shear.)

In the question they have given the area of cross section. But that also doesn't affect the forces. But it will affect the stress.

The significance of cross section comes to play when there are bending stress and torsional stress . Because they're independent on area of cross section but they depends on ( modulus of section or polar modulus of section) in that case we can check for the effect of cross sections.

Other than that the direct force calculations doesn't depend on cross sections. And the direct stress calculations depend on area of cross section and not on shape or symmetry of sections..

I am sure the student can understand the concept but in case of any doubts let me know in the comments..