Frames & machines worksheet with answers

Free printable Frames & machines worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
OAB120 NQ = ?300 mm75 mm

The bell crank shown turns about the pin O. A vertical force of 120 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 75 mm above O. Find Q.

F = 120 NOA = 300 mmOB = 75 mm
Q = N
2.Easy
OAB50 NQ = ?100 mm100 mm

The bell crank shown turns about the pin O. A vertical force of 50 N acts at A, 100 mm from O, and is balanced by a horizontal force Q at B, 100 mm above O. Find Q.

F = 50 NOA = 100 mmOB = 100 mm
Q = N
3.Medium
8 kN1 m1.5 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 8 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 8 kNAD = 1 mAB = 2.5 mAC = 1.5 m
A = kN
4.Medium
5 kN4 m4 m1.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 4 m above the ground and 1.8 m to the right of A. A vertical load of 5 kN acts on member AB at K, 1.08 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 4 mH = 4 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 1.08 m
FBC = kN
5.Hard
4 kN3 m1.2 m1.8 m0.9 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3 m apart, with its apex pin C 3 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.9 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 3 mheight of C = 3 mheight of DE = 1.2 mhorizontal distance A to K = 0.9 m
C = kN
6.Hard
8 kN0.5 kN4 m2 mABC

A uniform horizontal boom AB of weight 0.5 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2 m above A. A load of 8 kN hangs at B. Find the magnitude of the pin reaction A.

W = 8 kNWb = 0.5 kNAB = 4 mAC = 2 m
A = kN

Answer key

  1. 1. Q = 480 N
  2. 2. Q = 50 N
  3. 3. A = 17.94 kN
  4. 4. FBC = 1.541 kN
  5. 5. C = 1.562 kN
  6. 6. A = 16.5 kN

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