Axial Load Calculator
Plan your structural engineering project with our free axial load calculator. Get precise measurements, material lists, and budgets.
Reviewed by Abdullah, Technical Content Specialist
Formula
Stress = P/A; Deformation = PL/(AE); Safety Factor = Fy*A/P
Axial stress equals force divided by cross-sectional area. Axial deformation equals force times length divided by area times elastic modulus. The safety factor is the yield force (yield strength times area) divided by the applied force. Strain is deformation divided by original length.
Worked Examples
Example 1: Steel Column Under Compression
Problem:A W8x31 steel column (A = 9.12 sq in, Fy = 36 ksi) carries 50,000 lbs over 10 ft. Find stress and deformation.
Solution:Stress = 50,000 / 9.12 = 5,482 psi = 5.48 ksi\nDeformation = (50,000 x 120) / (9.12 x 29,000,000) = 0.0227 in\nYield force = 36 x 9.12 x 1,000 = 328,320 lbs\nSafety factor = 328,320 / 50,000 = 6.57
Result:5.48 ksi stress, 0.0227 in deformation, SF = 6.57
Example 2: Steel Tension Rod
Problem:A 1-inch diameter rod (A = 0.785 sq in) carries 20,000 lbs tension over 60 in. Fy = 36 ksi.
Solution:Stress = 20,000 / 0.785 = 25,478 psi = 25.48 ksi\nDeformation = (20,000 x 60) / (0.785 x 29,000,000) = 0.0527 in\nUtilization = 25.48 / 36 = 70.8%
Result:25.48 ksi stress, 0.053 in elongation, 70.8% utilized
Frequently Asked Questions
What is axial load and axial stress?
An axial load is a force applied along the longitudinal axis of a structural member, either in tension (pulling apart) or compression (pushing together). Axial stress is the internal stress resulting from this load, calculated as force divided by the cross-sectional area (sigma = P/A). The units are typically psi or ksi in US customary, or MPa in metric. Axial stress is uniform across the cross section only if the load passes through the centroid of the section.
How do I calculate axial deformation?
Axial deformation (elongation or shortening) is calculated using the formula delta = PL/(AE), where P is the applied force, L is the member length, A is the cross-sectional area, and E is the modulus of elasticity. For steel, E is approximately 29,000 ksi (200 GPa). The deformation is proportional to load and length, and inversely proportional to area and stiffness. This formula assumes the material remains in the elastic range and the member has a constant cross section.
What is a safe factor of safety for axial loading?
AISC steel design typically uses a safety factor of 1.67 for tension members (LRFD uses phi = 0.9) and 1.67-2.0 for compression depending on slenderness. ACI concrete design uses higher factors. For general structural applications, a factor of safety of 2.0 or greater against yield is conservative. Critical applications like bridges, cranes, or earthquake-resistant structures may require factors of 2.5-4.0. The required safety factor depends on load uncertainty, consequences of failure, and applicable building codes.
What happens when axial stress exceeds the yield strength?
When axial stress exceeds the yield strength, the material enters plastic deformation, meaning it will not return to its original shape when the load is removed. For ductile materials like structural steel, the member will continue to elongate with minimal increase in load until strain hardening begins, eventually reaching the ultimate tensile strength before fracture. For compression members, exceeding yield can trigger buckling. Brittle materials like cast iron may fracture with little warning once the yield point is exceeded.
References
Reviewed by Abdullah, Technical Content Specialist · Editorial policy