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.
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Things you need
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 = (yqL^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.
Tips and warnings
- To find the moment of inertia formula for common shapes, consult any elementary strength of materials text.
- 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.
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