Leaning objectivesAfter 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

Axial Stress

axial F

A

FL

AE;

F= Axial Force (Newtons, N)A = Cross-Sectional Area Perpendicular to “F” (mm2)E = Young’s Modulus of Material, MPaL = Original Length of Component, mm

= Average Stress (N/mm2 or MPa)

= Total Deformation (mm)

AE = “Axial Stiffness of Component”

Direct Shear Stress

average

P

A

average = Avearge Shear Stress (MPa)P = Shear LoadA = Area of Material Resisting “P”

Examples of Direct Shear Stress

Bolted Joint withTwo Shear Planes.

P = 50 KND = 13 mm

avg = ?

Area of bolt (Ab) = D2 / 4 = 13)2 / 4 = 132.7 mm2

A resisting shear = 2 Ab

avg = P / 2Ab = 50000 N/ 2(132.7) mm2 = 188.4 MPa

D

Direct Shear II

175

150

1313

Fillet Weld

Find the load P, such that the stress in the weld does not exceed the allowable stress limit of 80 MPa.

9.2

Solution:

avg = P / Aw = 80 MPa

Aw = Throat x Total Length = (9.2)(175)(2) = 3217 mm2

P / 3217 = 80 MPaP = (3217)(80) N = 257386 N = 257 kN

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:

a) the stress in the bar, and

b) the extension under this load

Assume that the elastic modulus for aluminum is 70GPa.

Example #1 (solution)

a) The stress can be evaluated via the definition:

σ = F/ A = 1000N/(10mm×10mm)σ =1000N/400mm2=2.5MPa

b) The strain can now be found, thus:ε= σ/E=2.5MPa/70GPa

ε= 0.3714μm/mThe displacement can now be calculated:

Δ= εlo= 0.3714 ×10-6×400Δ =0.0142mm

Example #1 (simulation)

Numerical Analysis Examples

1. An aluminium beam of 20mm diameter and a length of is exposed an axial force of 1kN. Evaluate:

a) The direct stress

b) The shear stress

c) and the displacement.

2. 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

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

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: a) the stress

b) the strain, and

c) the extension

Assume the Young’s Modulus for steel 200GPa.