Axial Loading Calculator

When bars, cables or pillars are pulled or compressed in their longitudinal direction, two effects occur simultaneously. Internal stresses arise in the material that counteract the load and the length of the component changes. When it is pulled, it expands; when it is compressed, it shortens.

This calculation tool takes these two states into account. By entering the load and cross-section, the axial stress is displayed. In addition, by entering the length and material, deformation, elongation and stiffness are also shown.

What is an axial load?

An axial load is a force acting directly along the centerline of an object. A tensile load stretches the object while a compressive load squeezes it. Because the line of action passes through the centerline, the load is evenly distributed across the entire cross section and the whole behavior can be described with two simple equations.

The first quantity is stress. This is the internal force per unit area and can be used to judge whether a component will withstand the load. If the stress exceeds the material's yield strength, then the component will permanently deform or break. The second quantity is deformation, which is the actual change in length. It depends on the applied load, the shape of the component, and the stiffness of the material, and can be used to judge whether the motion of the component is within acceptable design limits.

Axial load versus radial load

It is easier to understand this by comparing axial loads with their opposite. An axial load acts parallel to the axis or longitudinal direction of a component and in its direction. A radial load acts perpendicular to the axis, pushing outward on the edges. A screw that is tightened experiences an axial load while a wheel bearing on an axle exerts a radial load. The formulas on this page are for the axial case, i.e., when the force direction coincides with the geometry.

Instructions for using the calculator:

Enter the load and cross-sectional area. With these two values you can calculate axial stress. To calculate deformation enter the original length and select a material. The calculation tool will automatically fill in the modulus of elasticity (Young's Modulus). The result panel is updated in real time as values are entered.

The material menu contains common values. Steel has a Young's Modulus of about 200 GPa, aluminum is about 69 GPa, and there are also copper, titanium, cast iron, brass, and concrete. If you select "Custom", then you can enter your own Young's Modulus. This method is required if you want to back-calculate the Young's Modulus from a measured strain. Each input field also supports back-calculating. If you leave one of the fields for load, area, length, stress or deformation blank and enter the remaining required data, then the calculator will calculate the value for the blank field.

Understanding of formula.

Axial stress is the value obtained when load is divided by cross-sectional area.

A steel rod with a diameter of 25 mm that is subjected to a tensile force of 50 kN has an area of approximately 4.909 x 10^-4 square meters, resulting in a stress of approximately 101.9 MPa. Since this value is well below the yield strength of steel (250 MPa), the rod is safe under tensile loading.

To calculate the deformation, length and stiffness must be taken into account. With regard to stress, the relationship between both becomes clearer. Strain is the value obtained by dividing the stress by the modulus of elasticity, while the change in length is the product of strain and original length.

Assume a steel bar is 2 m long and the modulus of elasticity E = 200 GPa.

The calculated elongation would be approximately 1.02 mm.

The product AE represents the axial stiffness, or ability of the entire bar to resist an applied tensile force. Dividing this by length gives the axial spring constant which indicates the required load for a given amount of deflection. A thicker bar or a stiffer material will result in less deformation with the same applied force.

Strain links these two results together. It is the deformation per unit length and Hooke's law relates strain to stress through the modulus of elasticity.

The table below lists the names of each symbol and example values.

Check safety factor:

Stress itself is only meaningful when compared to the allowable stress of a material. When you enable the safety check and enter the yield strength, the calculator will calculate the safety factor by dividing the yield strength by the applied stress. If the value is greater than one, then the part remains in an elastic state. Engineers usually prefer to build in some margin to account for overloads, fatigue, and uncertainties in input values. The summary table shows the applied stresses side-by-side with the yield strengths of various materials so you can assess your stress levels at a glance.

Axial force applications

Axial members are found everywhere if you look closely enough. Cables holding up lighting fixtures are in pure tension and if they are too thin the stress will exceed the material's yield strength. Columns on the ground floor of a skyscraper are in pure compression carrying the weight of all floors above them. Struts inside airplane wings, pre-tensioned bolts, suspension cables for bridges, legs of chairs, and connecting rods in engines are also examples of this type of member. In these members you can observe whether or not the material is holding up to the stress by looking at deformation and how much it deforms under load.

Tips for accurate results

Be aware of the units. A megapascal is a newton per square millimeter. This is the conversion that engineers most commonly use. One gigapascal equals one thousand megapascals. The unit menus in each field ensure that the units for load, area, length and pressure are correct so no manual conversions are required. For threaded bars or bolts, use the net cross-sectional area instead of nominal cross-section because the threads actually reduce the effective cross-sectional area.

There are two important caveats to the use of these formulas: long members subjected to compressive forces can become unstable and buckle before reaching their yield strength. Such members require a separate Euler's critical load calculation. In addition, the linear formula is only valid so long as the material remains in an elastic state. If the applied stress exceeds the proportional limit, deformation becomes nonlinear, and simple relationships no longer apply.