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
10 kN0.8 m1.2 m0.8 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.8 m below A. A load of 10 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 10 kNAD = 0.8 mAB = 2 mAC = 0.8 m
FCD = kN
2.Easy
2 kN4 m0.6 m1.8 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, 2.4 m high, and are tied together by the horizontal bar DE at a height of 0.6 m. A load of 2 kN acts at C. Find the tension T in the tie DE.

P = 2 kNAB = 4 mheight of C = 2.4 mheight of DE = 0.6 m
T = kN
3.Medium
5 kN4 m2 m1.2 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 m above the ground and 1.2 m to the right of A. A vertical load of 5 kN acts on member AB at K, 0.48 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 4 mH = 2 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.48 m
FBC = kN
4.Medium
OAB300 NQ120 mm60 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 300 N at A (120 mm from O) is balanced by a horizontal force at B (60 mm above O). Find the magnitude of the pin reaction FO.

F = 300 NOA = 120 mmOB = 60 mm
FO = N
5.Hard
8 kN1 kN6 m2 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 m above A. A load of 8 kN hangs at B. Find the magnitude of the pin reaction A.

W = 8 kNWb = 1 kNAB = 6 mAC = 2 m
A = kN
6.Hard
w = 1 kN/m8 kN2 m2 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 1 kN/m over its full length and a point load of 8 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 8 kNAD = 2 mAB = 4 mAC = 0.5 m
FCD = kN

Answer key

  1. 1. FCD = 35.36 kN
  2. 2. T = 1.111 kN
  3. 3. FBC = 1.032 kN
  4. 4. FO = 670.8 N
  5. 5. A = 25.5 kN
  6. 6. FCD = 82.46 kN

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