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
4 kN1.2 m1.8 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 4 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 4 kNAD = 1.2 mAB = 3 mAC = 0.5 m
FCD = kN
2.Easy
OAB100 NQ = ?150 mm50 mm

The bell crank shown turns about the pin O. A vertical force of 100 N acts at A, 150 mm from O, and is balanced by a horizontal force Q at B, 50 mm above O. Find Q.

F = 100 NOA = 150 mmOB = 50 mm
Q = N
3.Medium
OAB120 NQ200 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 120 N at A (200 mm from O) is balanced by a horizontal force at B (100 mm above O). Find the magnitude of the pin reaction FO.

F = 120 NOA = 200 mmOB = 100 mm
FO = N
4.Medium
20 kN4 m1 m1.4 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 2.4 m high and the horizontal tie DE 1 m above the ground. A vertical load of 20 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the tension T in the tie.

P = 20 kNAB = 4 mheight of C = 2.4 mheight of DE = 1 mhorizontal distance A to K = 1.5 m
T = kN
5.Hard
w = 4 kN/m2 kN0.6 m1.4 m0.75 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.75 m below A). The beam carries a uniform load of 4 kN/m over its full length and a point load of 2 kN at its free end B. Find the force FCD in the strut.

w = 4 kN/mP = 2 kNAD = 0.6 mAB = 2 mAC = 0.75 m
FCD = kN
6.Hard
F = ?1000 N20 mmABC

A toggle press has two equal links AB and BC, each 120 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 1000 N at the slider C? Neglect friction and weights.

Q = 1000 NAB = BC = 120 mmh = 20 mm
F = N

Answer key

  1. 1. FCD = 26 kN
  2. 2. Q = 300 N
  3. 3. FO = 268.3 N
  4. 4. T = 10.71 kN
  5. 5. FCD = 25.61 kN
  6. 6. F = 338.1 N

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