Tensile Stress Calculator

Tensile stress is the internal stress that develops in a material when it is pulled in tension. It is defined as the applied tensile force divided by the cross-sectional area perpendicular to the force: sigma = F / A. Units are psi (lb/in^2) or MPa (N/mm^2). Compressive stress uses the same formula but the force pushes rather than pulls. Tensile and compressive stress are both types of normal stress.

The safety factor (SF) is the ratio of the material's ultimate tensile strength (or yield strength) to the actual calculated stress: SF = Fu / sigma. For structural steel, SF against yielding = Fy / sigma. Typical safety factors in allowable stress design are 1.5-2.5 against yielding and 2.0-3.5 against fracture, depending on the application and consequences of failure.

Yield strength (Fy) is the stress at which a material begins to deform plastically (permanently). Above Fy, the material does not return to its original shape when unloaded. Ultimate tensile strength (Fu) is the maximum stress the material can withstand before fracture. For ASTM A36 steel: Fy = 36 ksi, Fu = 58-80 ksi. Structural design limits stress below Fy for ductile behavior.

Tensile capacity = Fy x A (for gross section yielding). Doubling the area doubles the tensile capacity. For members with holes (bolt holes, perforations), the net area must be used: A_net = A_gross - (hole diameter x thickness). Net section fracture capacity = Fu x A_net x 0.85 (per AISC). The controlling limit state is the smaller of gross yield or net fracture.

Elongation = (F x L) / (A x E), where F is the applied force, L is the original length, A is the cross-sectional area, and E is Young's modulus. This is Hooke's Law applied to axial deformation. For a 1-inch diameter steel rod (E = 29,000 ksi, A = 0.785 sq in), 10,000 lb load, 12-inch length: elongation = (10,000 x 12) / (0.785 x 29,000,000) = 0.0053 inches.