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Problem 3.156

10 lb. A couple of magnitude M = 54 lb . in. and the three forces shown are applied to an angle bracket. (a) Find the resultant of this system of forces. (b) Locate the points where the line of action of the resultant intersects line AB and line BC . 30 lb. 12 in. 60 o. A. B. M.

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Problem 3.156

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  1. 10 lb A couple of magnitude M = 54 lb.in. and the three forces shown are applied to an angle bracket. (a) Find the resultant of this system of forces. (b) Locate the points where the line of action of the resultant intersects line AB and line BC. 30 lb 12 in 60o A B M 8 in C 45 lb Problem 3.156

  2. Problem 3.156 Solving Problems on Your Own 10 lb A couple of magnitude M = 54 lb.in. and the three forces shown are applied to an angle bracket. (a) Find the resultant of this system of forces. (b) Locate the points where the line of action of the resultant intersects line AB and line BC. 30 lb 12 in 60o A B M 8 in C 45 lb 1. Determine the resultant of two or more forces. Determine the rectangular components of each force. Adding these components will yield the components of the resultant.

  3. Problem 3.156 Solving Problems on Your Own 10 lb 30 lb A couple of magnitude M = 54 lb.in. and the three forces shown are applied to an angle bracket. (a) Find the resultant of this system of forces. (b) Locate the points where the line of action of the resultant intersects line AB and line BC. 12 in 60o A B M 8 in C 45 lb 2. Reduce a force system to a force and a couple at a given point. The force is the resultant R of the system obtained by adding the various forces. The couple is the moment resultant of the system M, obtained by adding the moments about the point of the various forces. R = SFM = S ( rxF )

  4. Problem 3.156 Solving Problems on Your Own 10 lb 30 lb A couple of magnitude M = 54 lb.in. and the three forces shown are applied to an angle bracket. (a) Find the resultant of this system of forces. (b) Locate the points where the line of action of the resultant intersects line AB and line BC. 12 in 60o A B M 8 in C 45 lb 3. Reduce a force and a couple at a given point to a single force. The single force is obtained by moving the force until its moment about the point (A) is equal to the couple vector MA. A position vector r from the point, to any point on the line of action of the single force R must satisfy the equation rxR = MA R R

  5. 10 lb Problem 3.156 Solution 30 lb 12 in 60o A B M 8 in C 45 lb SF : R = ( _ 10 j ) + (_ 45 i ) + ( 30 cos 60oi + 30 sin 60oj ) = _ ( 30 lb ) i + ( 15.98 lb ) j R = 34.0 lb 28.0o Determine the resultant of two or more forces. (a) Adding the components of the forces:

  6. 10 lb Problem 3.156 Solution 30 lb 12 in 60o A B M 8 in C 45 lb + Reduce a force system to a force and a couple at a given point. (b) First reduce the given forces and couple to an equivalent force-couple system (R, MB) at B. SMB : MB = ( 54 lb.in ) + ( 12 in )(10 lb) _ ( 8 in ) ( 45 lb) = _ 186 lb.in

  7. Problem 3.156 Solution a A D B c R E C + + Reduce a force and a couple at a given point to a single force. With R at D: SMB : _ 186 lb.in = _a ( 15.9808 lb) ora = 11.64 in and with RatE SMB : _ 186 lb.in = c ( 30 lb) orc = 6.20 in The line of action of R intersects line AB 11.64 in. to the left of B and intersects line BC 6.20 in below B.

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