Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter5: Stresses In Beams (basic Topics)
Section: Chapter Questions
Problem 5.9.5P: A sign for an automobile service station is supported by two aluminum poles of hollow circular cross...
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D
P
B
A
C
L
L
2
2
Figure 5
The A-36 steel structure consists two roller-connected prismatic beams with equal cross-
sections, as shown in Figure 5 where L=6 m. The structure has to support a force P=30 kN.
Neglect the weight of the beams and the friction in the roller connection B.
a) Find the vertical internal force in the roller connection B. HINT: declare the roller
connection in B as redundant, and separate the structure into 2 beams.
b) Find the support reactions in the fixed end D, in the pin C, and in the roller A.
c) Plot the shear force diagram and the bending moment diagrams of the two beams.
Determine Mmax and Vmax for the structure.
d) Select the lightest-weight standard wide-flange beam that will safely support the
loading without plastic deformations. The allowable bending stress is 170 MPa and
the allowable shear stress is 100 MPa.
e)
Calculate the vertical displacement at B and the slopes at A and C.
f) Write the equation of the elastic curve for the region BC.
Transcribed Image Text:D P B A C L L 2 2 Figure 5 The A-36 steel structure consists two roller-connected prismatic beams with equal cross- sections, as shown in Figure 5 where L=6 m. The structure has to support a force P=30 kN. Neglect the weight of the beams and the friction in the roller connection B. a) Find the vertical internal force in the roller connection B. HINT: declare the roller connection in B as redundant, and separate the structure into 2 beams. b) Find the support reactions in the fixed end D, in the pin C, and in the roller A. c) Plot the shear force diagram and the bending moment diagrams of the two beams. Determine Mmax and Vmax for the structure. d) Select the lightest-weight standard wide-flange beam that will safely support the loading without plastic deformations. The allowable bending stress is 170 MPa and the allowable shear stress is 100 MPa. e) Calculate the vertical displacement at B and the slopes at A and C. f) Write the equation of the elastic curve for the region BC.
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