Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 30-in-long bronze [E = 15900 ksi, a = 9.4x 10-6/°F] bar with a cross-sectional area of 1.00 in.?. Bar (2) is a 48-in-long aluminum alloy [E = 9200 ksi, a = 12.6 x 10-6/°F] bar with a cross-sectional area of 2.50 in.?. Both bars are unstressed before the load Pis applied. Assume L1=30 in., L2=48 in., a=32 in., b-44 in., and c-14 in. If a concentrated load of P = 29 kips is applied to the rigid bar at Dand the temperature is decreased by 120°F, determine: (a) the normal stresses in bars (1) and (2). (b) the normal strains in bars (1) and (2). (c) the deflection of the rigid bar at point D. L2 A B C D L1 (1) b

Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 30-in-long bronze [E = 15900 ksi, a = 9.4x 10-6/°F] bar with a cross-sectional area of 1.00 in.?. Bar (2) is a 48-in-long aluminum alloy [E = 9200 ksi, a = 12.6 x 10-6/°F] bar with a cross-sectional area of 2.50 in.?. Both bars are unstressed before the load Pis applied. Assume L1=30 in., L2=48 in., a=32 in., b-44 in., and c-14 in. If a concentrated load of P = 29 kips is applied to the rigid bar at Dand the temperature is decreased by 120°F, determine: (a) the normal stresses in bars (1) and (2). (b) the normal strains in bars (1) and (2). (c) the deflection of the rigid bar at point D. L2 A B C D L1 (1) b

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 30-in.-long bronze [E = 15900 ksi,
9.4x 10-6/°F] bar with a cross-sectional area of 1.00 in.?. Bar (2) is a 48-in-long aluminum alloy [E = 9200 ksi, a = 12.6 x
10-6/°F] bar with a cross-sectional area of 2.50 in.?. Both bars are unstressed before the load Pis applied. Assume L1=30 in., L2=48
a =
%3D
in., a=32 in., b=44 in., and c=14 in. If a concentrated load of P = 29 kips is applied to the rigid bar at Dand the temperature is
decreased by 120°F, determine:
(a) the normal stresses in bars (1) and (2).
(b) the normal strains in bars (1) and (2).
(c) the deflection of the rigid bar at point D.
(2)
L2
A
B
D
L1
(1)

Assume the rigid bar ABCD rotates clockwise around point A. Using a deflection sketch, relate the deflections of points B and C.
Assume positive deflections are down.
Answer: VB =
VC-
Relate the deformations of member (1) and member (2).
Answer: 81 =
i
82.
Using the relationships for deformation in terms of force and temperature change for each member together with Eqn. (3), derive
a compatibility equation for the structure.
+ a¡AT¡Li] =
F2L2
+ azAT¿L2
Answer:
i
[A2E2
Solve for F2 and F1 using the results from parts 1 and 4.
Answers: F1 =
i
! kips, F2 =
i
! kips.

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