How to calculate / formula for?

Question

strengths / load withstanding for rectangular pipes, square cross sections, beams, plates ,sheets

Answer 1

Get a strength and materials book.  That will help you get an understanding of the stress that the material has and if you can find one, get a ASD Manual (Allowable Stress Design Manual) to calculate strength of beams and pipes.  If you want plates and shells, get a book by Steven Timoshenko called Plates and Shells or you can do like most engineers do and use a software to approximate the stresses and strains in materials like ANSI.    What you are asking for is kind of out of scope in answering a question like this because there isnt one equation for anything but many equations and you have to know how to apply those equations because whenever you are talking about the strength of a structural member, you have to talk about end conditions, supports and how loads are acting on members.  You have to understand statics and strength of material.  If you are a college student asking this question and have taken the course above, ask a professor if they have a manual to help you out with the equations.  It is too numerous to lay them out here.

Answer 2

The equation for tensile or compressive stress is relatively easy, stress = area / load.  Generally speaking (and this is very general) the calculated stress should be about 1/3 of a materials yield strength.  Yield strength or tensile yield strength as it sometimes called can be found on matweb.com.

Bending stresses are not something I can give a quick answer on.

The sometimes tricky part is getting the cross-sectional area of the member being loaded.  For pipes, square sections and the like, just calculate the cross-sectional area.  For beams and the like a AISC manual has all of those in it.  You could probably just google the section and find an answer too.

This answer is in no way a substitute for a proper engineering education or at the very least a strengths of materials course.