The assembled structure in Figure 1 consists of two beams (A-B and B-D). The L-long member A-B and the 2L-long member B-D are connected by an internal hinge at B. A-B is fixed onto a wall at point A and B-D has a simple roller support at point D. Note that A-D is subjected to a uniform distributed load of intensity q from A to D as shown in the figure. The two members have the same uniform cross section and are made of the same material (i.e., El for both members A-B and B-D is identical and constant). Take L = 3 m and q = 1.5 kN/m. A q D B C Moment ➤ X L release L Figure 1 a) Find an expression for Elv(x) in the compound beam A-D from points A to D using the method of integration. v(x) is the elastic curve for A-D and x is a horizonal coordinate from point A (x=0 m) to D (x=9 m). Hint: the hinge at ensures deflection is continuous there, but the slope can be discontinuous; hence, the deflection needs to be split into two: an expression valid between A and B and another one valid between B and D. b) Plot Elv(x) from A to D using appropriate computer software. c) Determine the maximum value of Elv(x) due to the distributed load q and its location with respect to point A.
The assembled structure in Figure 1 consists of two beams (A-B and B-D). The L-long member A-B and the 2L-long member B-D are connected by an internal hinge at B. A-B is fixed onto a wall at point A and B-D has a simple roller support at point D. Note that A-D is subjected to a uniform distributed load of intensity q from A to D as shown in the figure. The two members have the same uniform cross section and are made of the same material (i.e., El for both members A-B and B-D is identical and constant). Take L = 3 m and q = 1.5 kN/m. A q D B C Moment ➤ X L release L Figure 1 a) Find an expression for Elv(x) in the compound beam A-D from points A to D using the method of integration. v(x) is the elastic curve for A-D and x is a horizonal coordinate from point A (x=0 m) to D (x=9 m). Hint: the hinge at ensures deflection is continuous there, but the slope can be discontinuous; hence, the deflection needs to be split into two: an expression valid between A and B and another one valid between B and D. b) Plot Elv(x) from A to D using appropriate computer software. c) Determine the maximum value of Elv(x) due to the distributed load q and its location with respect to point A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The assembled structure in Figure 1 consists of two beams (A-B and B-D). The L-long member A-B
and the 2L-long member B-D are connected by an internal hinge at B. A-B is fixed onto a wall at
point A and B-D has a simple roller support at point D. Note that A-D is subjected to a uniform
distributed load of intensity q from A to D as shown in the figure. The two members have the same
uniform cross section and are made of the same material (i.e., El for both members A-B and B-D is
identical and constant).
Take L = 3 m and q = 1.5 kN/m.
A
q
D
B
C
Moment
➤ X
L
release
L
Figure 1
a) Find an expression for Elv(x) in the compound beam A-D from points A to D using the
method of integration. v(x) is the elastic curve for A-D and x is a horizonal coordinate
from point A (x=0 m) to D (x=9 m). Hint: the hinge at ensures deflection is continuous
there, but the slope can be discontinuous; hence, the deflection needs to be split into two:
an expression valid between A and B and another one valid between B and D.
b) Plot Elv(x) from A to D using appropriate computer software.
c) Determine the maximum value of Elv(x) due to the distributed load q and its location
with respect to point A.
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