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
OAB80 NQ = ?200 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 80 N acts at A, 200 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 80 NOA = 200 mmOB = 60 mm
Q = N
2.Easy
8 kN4.8 m1.2 m1.3 m0.6 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 8 kN acts on leg AC at the point K, 0.6 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 8 kNAB = 4.8 mhorizontal distance A to K = 0.6 m
By = kN
3.Medium
2 kN2.4 m1.5 m3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart. The legs meet at the pin C, 4.5 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 2 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 2 kNAB = 2.4 mheight of C = 4.5 mheight of DE = 1.5 m
C = kN
4.Medium
OAB200 NQ240 mm120 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 200 N at A (240 mm from O) is balanced by a horizontal force at B (120 mm above O). Find the magnitude of the pin reaction FO.

F = 200 NOA = 240 mmOB = 120 mm
FO = N
5.Hard
20 kN6 kN3 m2 m0.45 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 2 m high and 0.45 m to the right of A. Member AB carries a vertical load of 20 kN at K, 0.225 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 20 kNQ = 6 kNL = 3 mH = 2 mhorizontal distance A to B = 0.45 mhorizontal distance A to K = 0.225 m
Ax = kN
6.Hard
6 kN1.5 kN6 m4 mABC

A uniform horizontal boom AB of weight 1.5 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 4 m above A. A load of 6 kN hangs at B. Find the magnitude of the pin reaction A.

W = 6 kNWb = 1.5 kNAB = 6 mAC = 4 m
A = kN

Answer key

  1. 1. Q = 266.7 N
  2. 2. By = 1 kN
  3. 3. C = 1.077 kN
  4. 4. FO = 447.2 N
  5. 5. Ax = 1.012 kN
  6. 6. A = 10.15 kN

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