The strain in an axially loaded bar is defined as: Strain is positive in tension (D>0 means e<0) and negative in compression (D<0); Strain is a non-dimensional length – a fraction. Because strain is small, it is often given as a percentage by multiplying by 100%: e.g., e = 0.003 = 0.3%.

The simplest formula for axial stress is force divided by cross-sectional area.

Compressive stress is axial stress that tends to cause a body to become shorter along the direction of applied force. Tensile stress is axial stress that tends to cause a body to become longer along the direction of applied force. Compare shear stress strain.

The force that acts along the central axis of the body is known as axial force. There will be a decrease in cross section area of the body. When the body will be subjected to excessive axial compression force, the failure occurs due to crushing of the body.

Axial stress is defined by Eq. (4.64):(4.64)σa=FeAs+σbwhere σa=total axial stress (psi), Fe=effective tension/compression (lbf), As=cross-sectional area (in. 2), σb=bending stress (psi).

The formula to calculate compressive strength is F = P/A, where:

1. F=The compressive strength (MPa)
2. P=Maximum load (or load until failure) to the material (N)
3. A=A cross section of the area of the material resisting the load (mm2)

Calculating Compressive Strength The formula is: CS = F ÷ A, where CS is the compressive strength, F is the force or load at point of failure and A is the initial cross-sectional surface area.

A general formula for axial force is Ned equals 270 times KN, where E equals 7,000 times MPA, KN equals 1,000 times Newton and d equals 640.3 times mm.

M = bending moment (Nm, lb in) I = moment of Inertia (m 4, mm 4, in 4) The maximum moment in a cantilever beam is at the fixed point and the maximum stress can be calculated by combining 1b and 1d to. σ max = y max F L / I (1e) Example – Cantilever Beam with Single Load at the End, Metric Units

The relative values of the tension and compression strain are dependant on the location of the neutral axis for bending, which is in turn dependant on the shape of the cantilever’s cross-section. The cantilever method assumed that the whole frame will deform laterally in the same way as the vertical cantilever.

The linear axial stress profile for a sample structure is shown at the bottom of Figure 7.8. If we assume an unknown value for the stress in the left column ( σ 1 in the figure) then the cantilever method can be used to find the stress in the other two columns as a function of their relative distance from the neutral axis as shown in the figure.

For a cantilever beam that carries only transverse loads, the axial force is always zero, provided the deflections are small. Therefore it is rather common to neglect axial forces. The calculated results in this page are based on the following assumptions: