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
OAB150 NQ = ?300 mm50 mm

The bell crank shown turns about the pin O. A vertical force of 150 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 50 mm above O. Find Q.

F = 150 NOA = 300 mmOB = 50 mm
Q = N
2.Easy
2 kN1.2 m2.4 m1.2 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.2 m below A. A load of 2 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 2 kNAD = 1.2 mAB = 3.6 mAC = 1.2 m
FCD = kN
3.Medium
10 kN5 m2.5 m3 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 5 m apart, and B is 2.5 m above the ground and 3 m to the right of A. A vertical load of 10 kN acts on member AB at K, 0.75 m (horizontally) from A. Find the force FBC in member BC.

P = 10 kNL = 5 mH = 2.5 mhorizontal distance A to B = 3 mhorizontal distance A to K = 0.75 m
FBC = kN
4.Medium
150 NQ = ?15°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 15° with the line AC. A downward force of 150 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 150 Nθ = 15°
Q = N
5.Hard
F = ?2500 N25 mmABC

A toggle press has two equal links AB and BC, each 200 mm long between pins. The joint B sits 25 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 2500 N at the slider C? Neglect friction and weights.

Q = 2500 NAB = BC = 200 mmh = 25 mm
F = N
6.Hard
12 kN2 kN4 m2.5 m0.6 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 2.5 m high and 0.6 m to the right of A. Member AB carries a vertical load of 12 kN at K, 0.36 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 = 12 kNQ = 2 kNL = 4 mH = 2.5 mhorizontal distance A to B = 0.6 mhorizontal distance A to K = 0.36 m
Ax = kN

Answer key

  1. 1. Q = 900 N
  2. 2. FCD = 8.485 kN
  3. 3. FBC = 1.921 kN
  4. 4. Q = 279.9 N
  5. 5. F = 629.9 N
  6. 6. Ax = 1.169 kN

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