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Statics: Find resultant force and couple moment

by Chandasouk
Tags: couple, force, moment, resultant, statics
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Chandasouk
#1
Mar9-13, 06:02 PM
P: 165


Calculate the resultant force’s magnitude and the couple moment.

Let a = 3.70 m
w1=5.35kN/m
w2=4.00kN/m

The resultant force of the triangle is 1/2(3.70)(5.35)=9.898 kN

The resultant force of the rectangle is (4)(3.70) = 14.8kN

So FR (The force's magnitude) is 24.69kN

I found the location of the triangle's load to be 1/3(3.7) = 1.233m

I found the location of the rectangles load to be 1/2(3.70)+3.7 = 5.550m

So I calculated the couple moment MRa (Taking counter clockwise to be POSITIVE) I get
(9.898)(1.233)+(14.8)(5.55) = 94.3kN*m

but when I put these answers down for MasteringEngineering, they are incorrect. Where did I go wrong?
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haruspex
#2
Mar9-13, 06:36 PM
Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,644
W1 and W2 are acting in opposite directions.
Even if you correct that your FR calculation will still be wrong. You don't want the total vertical force. You only want the load at A. To get that, take moments about B.
When you take moments about A for the second part, W1 has a negative moment. (I assume it's only asking for the moment about A due to W1 and W2. If the joint at B is holding the beam then there will also be a moment from that, and the total moment will be zero.)
haruspex
#3
Mar9-13, 06:36 PM
Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,644
W1 and W2 are acting in opposite directions.
Even if you correct that your FR calculation will still be wrong. You don't want the total vertical force. You only want the load at A. To get that, take moments about B.
When you take moments about A for the second part, W1 has a negative moment. (I assume it's only asking for the moment about A due to W1 and W2. If the joint at B is holding the beam then there will also be a moment from that, and the total moment will be zero.)


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