1. Leaning objectives Axial Stress
After the session you will be able to use appropriate tools to evaluate the following:
Axial Stress
Tension and Compression
Axial displacement
Shear Stress
Double shear
Weld strength

2. s = Average Stress (N/mm2 or MPa)
Axial Stress
F= Axial Force (Newtons, N)
A = Cross-Sectional Area Perpendicular to “F” (mm2)
E = Young’s Modulus of Material, MPa
L = Original Length of Component, mm
s = Average Stress (N/mm2 or MPa)
D = Total Deformation (mm)
AE = “Axial Stiffness of Component”

3. Direct Shear Stress taverage = Avearge Shear Stress (MPa)
P = Shear Load
A = Area of Material Resisting “P”

4. Examples of Direct Shear Stress
Bolted Joint with
Two Shear Planes.
P = 50 KN
D = 13 mm
tavg = ?
Area of bolt (Ab) = p D2 / 4 = p (13)2 / 4 = mm2
A resisting shear = 2 Ab
tavg = P / 2Ab = N/ 2(132.7) mm2 = MPa

5. Direct Shear II Fillet Weld13 13
150
175
Fillet Weld
9.2
Find the load P, such that the stress in the weld does
not exceed the allowable stress limit of 80 MPa.

6. tavg = P / Aw = 80 MPa Solution: Aw = Throat x Total Length
= (9.2)(175)(2) = 3217 mm2
P / 3217 = 80 MPa
P = (3217)(80) N = N
= 257 kN

7. Example #1
A 20mm×20mm square cross-section aluminum bar is 400mm in length. If the bar is subjected to an 1kN pull; use MATLAB (or otherwise) calculate:
the stress in the bar, and
the extension under this load
Assume that the elastic modulus for aluminum is 70GPa.

8. The displacement can now be calculated:
Example #1 (solution)
The stress can be evaluated via the definition:
σ = F/ A = 1000N/(10mm×10mm)
σ =1000N/400mm2=2.5MPa
The strain can now be found, thus:
ε= σ/E=2.5MPa/70GPa
ε= μm/m
The displacement can now be calculated:
Δ= εlo= ×10-6×400
Δ =0.0142mm

9. Example #1 (simulation)

10. Numerical Analysis Examples
An aluminium beam of 20mm diameter and a length of is exposed an axial force of 1kN. Evaluate:
The direct stress
The shear stress
and the displacement.
A udl of 0.5kN/m is applied to a steel beam of 600mm, if the cross-section is 30x10mm evaluate the maximum bending stress. Also evaluate the maximum displacement of the beam

11. Summary Have we met our leaning objectives?
specifically: are you able to use appropriate tools to evaluate the following:
Axial Stress
Tension and Compression
Shear Stress
Bending
Tension/Compression & Shear
Beam deflexions

12. Examination type questions
A steel 20mm square cross-section bar is 0.75m in length. If the bar is subjected to an 20kN pull; use MATLAB (or otherwise) calculate:
the stress
the strain, and
the extension
Assume the Young’s Modulus for steel 200GPa.