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
OAB50 NQ = ?250 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 50 N acts at A, 250 mm from O, and is balanced by a horizontal force Q at B, 150 mm above O. Find Q.

F = 50 NOA = 250 mmOB = 150 mm
Q = N
2.Easy
8 kN2 m0.4 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 8 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 8 kNAD = 2 mAB = 2.4 mAC = 0.5 m
FCD = kN
3.Medium
200 NQ = ?10°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 10° with the line AC. A downward force of 200 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 200 Nθ = 10°
Q = N
4.Medium
3 kN1.2 m2.8 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 3 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 3 kNAD = 1.2 mAB = 4 mAC = 0.5 m
A = kN
5.Hard
8 kN5 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 high and 1.8 m to the right of A. Member AB carries a vertical load of 8 kN at K, 0.45 m (horizontally) from A, and a horizontal load of 5 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 8 kNQ = 5 kNL = 4 mH = 4 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.45 m
Ax = kN
6.Hard
15 kN2 kN4 m3 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 3 m high and 1.8 m to the right of A. Member AB carries a vertical load of 15 kN at K, 0.45 m (horizontally) from A, and a horizontal load of 2 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 15 kNQ = 2 kNL = 4 mH = 3 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.45 m
Ax = kN

Answer key

  1. 1. Q = 83.33 N
  2. 2. FCD = 39.58 kN
  3. 3. Q = 567.1 N
  4. 4. A = 25 kN
  5. 5. Ax = 1.755 kN
  6. 6. Ax = 0.3375 kN

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