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
12 kN3.2 m1.2 m3.3 m0.64 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3.2 m apart. A vertical load of 12 kN acts on leg AC at the point K, 0.64 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 12 kNAB = 3.2 mhorizontal distance A to K = 0.64 m
By = kN
2.Easy
10 kN5 m0.8 m2.2 m1 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 5 m apart. A vertical load of 10 kN acts on leg AC at the point K, 1 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 10 kNAB = 5 mhorizontal distance A to K = 1 m
By = kN
3.Medium
3 kN1.2 m0.8 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 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 = 2 mAC = 1.2 m
A = kN
4.Medium
OAB200 NQ300 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 200 N at A (300 mm from O) is balanced by a horizontal force at B (100 mm above O). Find the magnitude of the pin reaction FO.

F = 200 NOA = 300 mmOB = 100 mm
FO = N
5.Hard
F = ?1500 N20 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 20 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1500 N at the slider C? Neglect friction and weights.

Q = 1500 NAB = BC = 150 mmh = 20 mm
F = N
6.Hard
12 kN4 m0.8 m2.2 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 3 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 12 kN to the right acts at C. Find the tension T in the tie.

P = 12 kNAB = 4 mheight of C = 3 mheight of DE = 0.8 m
T = kN

Answer key

  1. 1. By = 2.4 kN
  2. 2. By = 2 kN
  3. 3. A = 5.385 kN
  4. 4. FO = 632.5 N
  5. 5. F = 403.6 N
  6. 6. T = 8.182 kN

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