A uniform horizontal beam with a length of l=8.00m and a weight of Wb=200N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53.0 with the beam(figure a).A person of weight Wp=600N stands on the beam. Let d represent the distance in meters between the person and the hinge at the left end of the beam.(see figure c) a)Show that the cable tension is given by T=93.9d+125, with T in Newton’s. b)Show that the direction angle of the hinge force is described by tan ? =(32/3d + 4 − 1)tan 53.0°. c)Show that the magnitude of the hinge force is given by R = root 8.82 103d 2 − 9.65 104d + 4.96 105. d)Describe how the changes in T, ?, and R as d increases differ from one another.
A uniform horizontal beam with a length of l=8.00m and a weight of Wb=200N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53.0 with the beam(figure a).A person of weight Wp=600N stands on the beam. Let d represent the distance in meters between the person and the hinge at the left end of the beam.(see figure c) a)Show that the cable tension is given by T=93.9d+125, with T in Newton’s. b)Show that the direction angle of the hinge force is described by tan ? =(32/3d + 4 − 1)tan 53.0°. c)Show that the magnitude of the hinge force is given by R = root 8.82 103d 2 − 9.65 104d + 4.96 105. d)Describe how the changes in T, ?, and R as d increases differ from one another.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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A uniform horizontal beam with a length of l=8.00m and a weight of Wb=200N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53.0 with the beam(figure a).A person of weight Wp=600N stands on the beam. Let d represent the distance in meters between the person and the hinge at the left end of the beam.(see figure c)
a)Show that the cable tension is given by T=93.9d+125, with T in Newton’s.
b)Show that the direction angle of the hinge force is described by tan ? =(32/3d + 4
− 1)tan 53.0°.
c)Show that the magnitude of the hinge force is given by
R = root 8.82 103d 2 − 9.65 104d + 4.96 105.
d)Describe how the changes in T, ?, and R as d increases differ from one another.
Transcribed Image Text:w,
W.
Rsin 0
T sin o
Rcos 0
T cos
W,
W.
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