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posted by  obscur on 10/3/2008 7:17:21 PM  |  status: Live  

statics

Course Textbook Chapter Problem
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Question Details:
A load of three forces, F1=75N, F2=100N, F3=80N, and a couple-moment M, are applied to the rigid bracket A, B, C, D. Which is in equilibrium with the support reactions at points A & C. Determine the X- and Y- support reaction forces:

a) Ax in Newtons
b) Ay in Newtons
c) Cx in Newtons
d) Cy in Newtons
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posted by EngAve on 10/4/2008 11:22:47 PM  |  status: Live
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Response Details:
a.) 
Made a mistake , so please see the corrected solution below.
Ax = (-F3)(cos45°) + (F1)(cos30) + F2 - 60Nm / (0.250m + 0.275m) 
Ax = (-80N)(cos45°)+(75N)(cos30) + 100N - 60Nm/(0.525m)
Ax = -44.7426 N
 
First, taking sum of all momments about point D, gives:
ΣMD = (F2)(.175m) - 60Nm - (Ax)(.250m+.275m) = 0
It equals zero, because the bracket is in equilibrium.  Only one unknown to solve for: Ax.
Ax = [(100N)(.175m) - 60Nm] / (0.525m)
Ax = (175Nm - 60Nm) / (0.525m)
Ax = 115Nm / 0.525m
Ax = 219.048 N pointing to the left
 
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posted by obscur on 10/5/2008 12:19:39 AM  |  status: Live
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yes, If you want to break them down into seperate answers, I will rate all of them as high as possible.

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posted by EngAve on 10/5/2008 1:18:01 AM  |  status: Live
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"thanks"
Response Details:
b.)
Taking sum of all momments about point C, yields:
ΣMC = (F3)(cos45°)(.175m+.150m) - (F1)(cos30°)(.175m+.150m) - (F2)(.150m) + Ay(.250m+.275m) = 0
The only unknown is Ay, so we solve Ay as follows:
 
Ay = -9.71716 N
The fact that the answer is negative, just means it's opposite to the way I assumed it would point.  I assumed Ay would point upwards, but it actually points downards.  So the answer is:
Ay = 9.71716 N pointing downards
 
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posted by EngAve on 10/5/2008 1:30:46 AM  |  status: Live
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obscur's comment:
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Response Details:
c.) & d.)
 
Cannot solve because the problem states the rigid bracket A,B,C,D is supported at points A&B - but the drawing shows the supports at A and C respectively.  I'm assuming it's a typo, and the problem asks for supports at A&C or the drawing is not labeled correctly, or the supports are not drawn correctly.  Please confirm which is the case, and I will solve part (c) and part (d) for you.  Thanks.
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posted by obscur on 10/5/2008 2:07:05 AM  |  status: Live
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Response Details:
I fixed the posted Question.  Sorry for the error.
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posted by EngAve on 10/5/2008 3:18:54 PM  |  status: Live
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Response Details:
c.)
Cx = 0 N
This is because you have a roller support at point C.  Roller supports only exert a force in the y-direction, and no force in the x-direction.
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posted by EngAve on 10/5/2008 3:37:15 PM  |  status: Live
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obscur's comment:
"thanks again"