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
2 kN0.8 m1.6 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 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 = 0.8 mAB = 2.4 mAC = 0.75 m
FCD = kN
2.Easy
O100 N100 NQ = ?90 mm25 mm

A hand squeezes the handles of a pair of pliers with 100 N each, 90 mm from the pin O. The jaws grip a bolt 25 mm from the pin. Find the gripping force Q on the bolt.

F = 100 Na = 90 mmb = 25 mm
Q = N
3.Medium
OAB250 NQ200 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 250 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 = 250 NOA = 200 mmOB = 100 mm
FO = N
4.Medium
12 kN3 m2.5 m1.35 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 2.5 m above the ground and 1.35 m to the right of A. A vertical load of 12 kN acts on member AB at K, 0.54 m (horizontally) from A. Find the force FBC in member BC.

P = 12 kNL = 3 mH = 2.5 mhorizontal distance A to B = 1.35 mhorizontal distance A to K = 0.54 m
FBC = kN
5.Hard
6 kN5 m1.5 m2.5 m1.875 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 5 m apart, with its apex pin C 4 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 6 kN acts on leg AC at K, 1.875 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 6 kNAB = 5 mheight of C = 4 mheight of DE = 1.5 mhorizontal distance A to K = 1.875 m
C = kN
6.Hard
12 kN1 kN2 m2.5 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2.5 m above A. A load of 12 kN hangs at B. Find the magnitude of the pin reaction A.

W = 12 kNWb = 1 kNAB = 2 mAC = 2.5 m
A = kN

Answer key

  1. 1. FCD = 8.773 kN
  2. 2. Q = 360 N
  3. 3. FO = 559 N
  4. 4. FBC = 2.588 kN
  5. 5. C = 3.182 kN
  6. 6. A = 10.01 kN

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