How to Calculate Maximum Stress

By Yvonne Bernard; Updated April 24, 2017
Understanding maximum stress is critical in infrastructure design.

Stress is so common in our fast-paced culture that the term "maximum stress" immediately brings to mind "breaking point." In the world of engineering, stress is a point function, a force distributed internally from within a body, and maximum stress is the amount of stress a material can withstand before a cross-sectional area starts to contract noticeably. This force distribution, or stress, is expressed in pressure units of force per unit area. Calculating the net force and moment acting on a surface many times requires integration.

Calculate the moment of inertia of the cross section. For a rectangular cross section, I = (bh^3)/12 where I = Moment of inertia, b = width and h = height. I varies with shape.

Gather all necessary information. This includes the uniform load q, the length of the beam L, the perpendicular distance of the load from the neutral axis y and moment of inertia I.

Calculate the maximum stress σ using the formula for maximum stress in a beam with uniform load supported on both ends: σ = (y_q_L^2)/8*I, where y = the perpendicular distance of the load from the neutral axis, q = the magnitude of the load, L = the length of the beam and I = the moment of inertia of the cross section.

Tip

To find the moment of inertia formula for common shapes, consult any elementary strength of materials text.

Warning

Watch the units as you perform the calculations. Remember the units of stress are N/m^2 (newtons per meter squared) in metric or psi (pounds per square inch) in English units.

About the Author

Yvonne Bernard began her writing career in 1994. She has written articles for “Design News” and published an engineering text book, “Environmental Engineering,” for McGraw-Hill. Bernard is also a member of several engineering societies. She has a Bachelor of Science in mechanical engineering from the University of Illinois.