In the graph: http://imageshack.us/photo/my-images/9/problem475.jpg/. The resultant couple moment is:
The moments are as follows:
-200 x 3/5 x 2' = -240 ft lb
-200 x 4/5 x 2' = -320 ft lb
+sin30 x 150 x 4' = + 300 ft lb
+cos30 x 150 x 4' = +520 ft lb
Total = -240 -320 +300 +520 = +260 ft lb clockwise
My question is: -200 for both forces, and why multiplied by 2 not 4? Also, why +sin30? I am confused with the signs. Please need help!
The moments are as follows:
-200 x 3/5 x 2' = -240 ft lb
-200 x 4/5 x 2' = -320 ft lb
+sin30 x 150 x 4' = + 300 ft lb
+cos30 x 150 x 4' = +520 ft lb
Total = -240 -320 +300 +520 = +260 ft lb clockwise
My question is: -200 for both forces, and why multiplied by 2 not 4? Also, why +sin30? I am confused with the signs. Please need help!
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It looks like they chose point B as the point about which to compute torques - you can choose any point on the structure for that.
It also appears that they chose the sign convention "+" for clockwise moments and "-" for counterclockwise. It doesnt matter which convention you use as long as you use it consistently..
In this case the top force F exerts a CCW moment about B, and so does the lower force F, so they are both negative moments. They exert a pure couple on the structure because the linear forces are equal and opposite, therefore exert no net linear force on the structure as a whole. .
The horizontal component of the lower force F is 3/5 of F and acts at a perpendicular distance from B of 2 ft.
The vertical component of the upper force F is 4/5 *F and acts at a perpendicular distance of 2 ft from B.
Same with the sin & cosine for the 150 lb forces.
It also appears that they chose the sign convention "+" for clockwise moments and "-" for counterclockwise. It doesnt matter which convention you use as long as you use it consistently..
In this case the top force F exerts a CCW moment about B, and so does the lower force F, so they are both negative moments. They exert a pure couple on the structure because the linear forces are equal and opposite, therefore exert no net linear force on the structure as a whole. .
The horizontal component of the lower force F is 3/5 of F and acts at a perpendicular distance from B of 2 ft.
The vertical component of the upper force F is 4/5 *F and acts at a perpendicular distance of 2 ft from B.
Same with the sin & cosine for the 150 lb forces.