Football goal posts are sometimes torn down in the excitement of a win, which for winning home teams causes needless expenses. For the goal post and dimensions shown below, the fans have managed to put on a load W (representing their weights) in the negative y -direction at the location shown. From past goal post tear downs you have noticed that typically the base fails at the ground shown by the red dot, or at the back cross bar by the green dot. Assume the post is made of steel with a modulus E, radius R, area A, moment of inertia I, and polar moment of inertia J. INCLUDE the effects of shear from bending for this problem.

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Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.8P
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(b) For stress element A write expressions for all stresses and label their directions. A is the red
element at the base of the pole on the positive x-face.
Oy= Mare XR
y
Oy
wA Job
sslog
A
Oc=
Cut side at the
Oc
base of the post
(c) Draw a free body diagram with a cut on the post between the vertical member that is secured in
the ground and the cross bar for element B showing all applied and reaction forces and
moments. Write expressions for the reaction forces and moments.
Ry-w=G Rs=W
Mo
ET zo
Weo-TB=0
I3=9W
Vw
Wx6-Moz =O
My =GW
(d) For stress element B write expressions for all stresses and label their directions. B is the green
element on the crossbar on the positive z-face.
y! O O, O
4W xA
%3D
Ixb
I xST
Ous = Ixr
qW XR
Cut side at the
crossbar junction
(e) Element A was located on the front side of the post (the positive x-face). Is this the most critical
stress location for a cut at the bottom of the post? Provide one sentence justifying your answer.
(No calculations are required for this part answer)
NO, bccouse at the heae of the
from tac Side they are pullins down an or W
toner the nost citicel Peint neold be
3/4
Transcribed Image Text:(b) For stress element A write expressions for all stresses and label their directions. A is the red element at the base of the pole on the positive x-face. Oy= Mare XR y Oy wA Job sslog A Oc= Cut side at the Oc base of the post (c) Draw a free body diagram with a cut on the post between the vertical member that is secured in the ground and the cross bar for element B showing all applied and reaction forces and moments. Write expressions for the reaction forces and moments. Ry-w=G Rs=W Mo ET zo Weo-TB=0 I3=9W Vw Wx6-Moz =O My =GW (d) For stress element B write expressions for all stresses and label their directions. B is the green element on the crossbar on the positive z-face. y! O O, O 4W xA %3D Ixb I xST Ous = Ixr qW XR Cut side at the crossbar junction (e) Element A was located on the front side of the post (the positive x-face). Is this the most critical stress location for a cut at the bottom of the post? Provide one sentence justifying your answer. (No calculations are required for this part answer) NO, bccouse at the heae of the from tac Side they are pullins down an or W toner the nost citicel Peint neold be 3/4
Football goal posts are sometimes torn down in the excitement of a win, which for winning home teams
causes needless expenses. For the goal post and dimensions shown below, the fans have managed to
put on a load W (representing their weights) in the negative y -direction at the location shown, From
past goal post tear downs you have noticed that typically the base fails at the ground shown by the red
dot, or at the back cross bar by the green dot. Assume the post is made of steel with a modulus E,
radius R, area A, moment of inertia I, and polar moment of inertia J. INCLUDE the effects of shear from
bending for this problem.
y
y
18 ft
B
6 ft
A
W
y
(a) Draw a free body diagram with a cut at the base of the post by element A showing all applied
and reaction forces and moments. Write expressions for the reaction forces and moments.
20 ft
10 ft
20 ft
B.
Transcribed Image Text:Football goal posts are sometimes torn down in the excitement of a win, which for winning home teams causes needless expenses. For the goal post and dimensions shown below, the fans have managed to put on a load W (representing their weights) in the negative y -direction at the location shown, From past goal post tear downs you have noticed that typically the base fails at the ground shown by the red dot, or at the back cross bar by the green dot. Assume the post is made of steel with a modulus E, radius R, area A, moment of inertia I, and polar moment of inertia J. INCLUDE the effects of shear from bending for this problem. y y 18 ft B 6 ft A W y (a) Draw a free body diagram with a cut at the base of the post by element A showing all applied and reaction forces and moments. Write expressions for the reaction forces and moments. 20 ft 10 ft 20 ft B.
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