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
6 kN0.6 m0.9 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 6 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 6 kNAD = 0.6 mAB = 1.5 mAC = 1.5 m
FCD = kN
2.Easy
O100 N100 NQ = ?100 mm30 mm

A hand squeezes the handles of a pair of pliers with 100 N each, 100 mm from the pin O. The jaws grip a bolt 30 mm from the pin. Find the gripping force Q on the bolt.

F = 100 Na = 100 mmb = 30 mm
Q = N
3.Medium
12 kN5 m2 m2.25 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 m above the ground and 2.25 m to the right of A. A vertical load of 12 kN acts on member AB at K, 0.9 m (horizontally) from A. Find the force FBC in member BC.

P = 12 kNL = 5 mH = 2 mhorizontal distance A to B = 2.25 mhorizontal distance A to K = 0.9 m
FBC = kN
4.Medium
4 kN2.4 m1.5 m2.5 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart. The legs meet at the pin C, 4 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 4 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 2.4 mheight of C = 4 mheight of DE = 1.5 m
C = kN
5.Hard
w = 5 kN/m12 kN1 m1 m1.2 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.2 m below A). The beam carries a uniform load of 5 kN/m over its full length and a point load of 12 kN at its free end B. Find the force FCD in the strut.

w = 5 kN/mP = 12 kNAD = 1 mAB = 2 mAC = 1.2 m
FCD = kN
6.Hard
w = 4 kN/m15 kN1.2 m1.2 m0.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.5 m below A). The beam carries a uniform load of 4 kN/m over its full length and a point load of 15 kN at its free end B. Find the force FCD in the strut.

w = 4 kN/mP = 15 kNAD = 1.2 mAB = 2.4 mAC = 0.5 m
FCD = kN

Answer key

  1. 1. FCD = 16.16 kN
  2. 2. Q = 333.3 N
  3. 3. FBC = 3.672 kN
  4. 4. C = 2.218 kN
  5. 5. FCD = 44.26 kN
  6. 6. FCD = 103 kN

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