Fundamentals of Deformable Bodies
Chapter 1
Simple Stress
One of the basic problems of the engineer is to select the proper material and correctly use and
proportion it so as to enable a structure or machine to do most efficiently what it is designed to do.
For this purpose, it is essential to determine the strength, stiffness, and other properties of materials.
A tabulation of the average properties of common metals is given in Table B-1.
Three Types of Simple Stress
1. Normal Stress
1.1. Compressive Stress
1.2. Tensile Stress
2. Shearing Stress
3. Bearing Stress
Normal Stress
Normal Stress =
Applied load
Cross − sec tional area
Compressive stress =
Tensile stress =
=
Compressive load
Cross − sec tional area
Tensile load
Cross − sec tional area
P
A
c =
Pc
Ac
t =
Pt
At
Example 1
Two bars of equal length but different materials are suspended from a common support as shown.
Bar 1
500 N
Bar 2
5000 N
Bars supporting maximum loads
Cross-sectional area of each bar:
A1 = 10 mm2
A2 = 1000 mm2`
500 N
1 =
= 50 MPa
10mm2
2 =
1 MPa = 1 N/mm2
1 psi = 1 lbF/in2
1 ksi = 1 kip/in2
1 kip = kilo pound-force = 1000 pound-force
5000 N
= 5 MPa
1000mm2
Thus the material of bar 1 is ten times as strong as the material of bar 2..wikipedia.org/wiki/Str
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Example 2
An aluminum tube is rigidly fastened between a bronze and steel as shown. Axial loads are applied
at the positions indicated. Determine the stress in each material.
Bronze
20 kN
Al
15 kN 15 kN
Material
Bronze
Al
Steel
Steel
10 kN
Area
(mm2)
700
1000
800
Length
(mm)
500
600
700
Stress in each section
(MPa)
28.6
5.0
12.5
Problem Set 1
1. Determine the largest weight which can be supported by the two wires as shown. The
stresses in wires AB and AC are not to exceed 100 MPa and 150 MPa, respectively. The
cross sectional areas of the two wires are 400 mm2 for wire AB and 200 mm2 for wire AC.
C
B
30º
A 45º
W
2. Determine the outside diameter of a hollow steel tube that will carry a tensile load of 500 kN at
a stress of 140 MN/m2. Assume the wall thickness to be one-tenth of the outside diameter.
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3. A 1000-kg homogeneous bar AB is suspended from two cables AC and BD, each with crosssectional area of 400 mm2 as shown. Determine the magnitude P and x of the largest
additional force which can be applied to the bar. The stresses in the cables AC and BD are
limited to 100 MPa and 50 MPa, respectively.
C
1.8 m
P
1.8 m
x
A
B
2m
4. For the truss as shown, determine the stress in members AC and BD. The cross-sectional
area of each member is 900 mm2.
B
2
D
F
1
3m
A
Hx
C
Ay
30 kN
E
G
70 kN
H
Hy
4 panels at 4 m = 16 m
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