Structural members that experience axial tensile loads need to be sized so that they do not deform or fail under those loads. Stress is the relationship of force over a unit area, and it allows for the comparison of material strengths independent of cross-sectional area. Every material has a theoretical ultimate strength and yield strength based on the properties of that material. Therefore, if an engineer is designing a structural component, he can select the material and component dimensions based on the anticipated loads of the system. For a given component and a known tensile load, the maximum tensile stress is straightforward to calculate.
For a member with a constant axial cross section, measure the cross section and calculate the cross-sectional area. For example, a member with a rectangular cross-section of 1 x 2 inches has a cross-sectional area of 2 square inches. A member with a circular diameter of 2 inches has a cross-sectional area of (1 inch x 1 inch x pi) 3.14 square inches.
For a member with a variable cross section, select the smallest cross section. For example, a tapered cylinder will have the smallest cross section at the narrowest end of the taper.
Divide the the applied load by the cross-sectional area to calculate the maximum tensile stress. For example, a member with a cross-sectional area of 2 in sq and an applied load of 1000 pounds has a maximum tensile stress of 500 pounds per square inch (psi).
- "Mechanics of Materials," Second Edition; Beer and Johnston; 1992