FIG. 1.4 Deformations produced by the components of internal forces and couples.
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Transcript of FIG. 1.4 Deformations produced by the components of internal forces and couples.
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AA
Rt
0lim
(1.1)
dA
dV
A
V
dA
dP
A
PAA
00
limlim
(1.2)
A
V
A
P
(1.3)
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FIG. 1.4 Deformations produced by the components of internal forces and couples
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FIG. 1.6 A bar loaded axially by (a) uniformly distributed load of intensity p; and (b) a statically equivalent centroidal force P = pA
A
P
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FIG. 1.7 Normal stress distribution in a strip caused by a concentrated load
ILLUSTRATING ST. VENANT’S PRINCIPLE
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FIG. 1.9 Determining the stresses acting on an inclined section of a bar
2cos
cos/
cos
A
P
A
P
2sin
2cossin
cos/
sin
A
P
A
P
A
P
(1.5a)
(1.5b)
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FIG. 1.10 Stresses acting on two mutually perpendicular inclined sections of a bar
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PROCEDURE FOR STRESS ANALYSIS
In general, finding the normal stress in an axially loaded member of a structure involves the
following steps:
•Equilibrium Analysis
•Computation of Stresses
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Sample Problem 1.1
The bar ABCD in Figure (a) consists of three cylindrical steel segments, each with a different cross-sectional area. Axial loads are applied as shown. Calculate the normal stress in each segment.
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Sample Problem 1.2
For the truss shown in Fig. (a), calculate the normal stresses in (1) member AC; and (2) member BD. The cross-sectional area of each member is 900 mm2.
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Sample Problem 1.3
Figure (a) shows a two-member truss supporting a block of weight W. The cross-sectional areas of the members are 800 mm2 for AB and 400 mm2 for AC. Determine the maxi- mum safe value of W if the working stresses are 110 MPa for AB and 120 MPa for AC.
(a)
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GUIDED PROBLEMS
Problem 1.1
The compound bar ABCD consists of three segments, each of a different material with different dimensions. Compute the stress in each segment when the axial loads are applied.
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Problem 1.2
Neglecting the weights of bars OAB and AC, determine the stress in the bar AC.
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Problem 1.3
The cross-sectional area of each member of the truss is 4.2 in2. Calculate the stresses in members CD and CF.