Transcript Equilibrium of Forces

Leaning objectives
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
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, MPa
L = Original Length of Component, mm

= Average Stress (N/mm2 or MPa)
 = Total Deformation (mm)
AE = “Axial Stiffness of Component”
Direct Shear Stress
 average

average
P
A
P

A
= Avearge Shear Stress (MPa)
= Shear Load
= Area of Material Resisting “P”
Examples of Direct Shear Stress
D
Bolted Joint with
Two Shear Planes.
P
D
= 50 KN
= 13 mm
avg = ?
Area of bolt (Ab) = p D2 / 4 = p (13)2 / 4 = 132.7 mm2
A resisting shear = 2 Ab
avg = P / 2Ab = 50000 N/ 2(132.7) mm2 = 188.4 MPa
Direct Shear II
13
150
13
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.
Solution:
avg = P / Aw = 80 MPa
Aw = Throat x Total Length
= (9.2)(175)(2) = 3217 mm2
P / 3217 = 80 MPa
P = (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:
the stress in the bar, and
b) the extension under this load
Assume that the elastic modulus for aluminum is
70GPa.
a)
Example #1 (solution)
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/m
The displacement can now be calculated:
Δ= εlo= 0.3714 ×10-6×400
Δ =0.0142mm
a)
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)
b)
c)
2.
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
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:
the stress
b) the strain, and
c) the extension
Assume the Young’s Modulus for steel 200GPa.
a)