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
15 kN1.6 m0.4 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 15 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 15 kNAD = 1.6 mAB = 2 mAC = 0.75 m
FCD = kN
2.Easy
20 kN4.8 m1.5 m2.1 m1.8 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 20 kN acts on leg AC at the point K, 1.8 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 20 kNAB = 4.8 mhorizontal distance A to K = 1.8 m
By = kN
3.Medium
OAB250 NQ100 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 250 N at A (100 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 250 NOA = 100 mmOB = 150 mm
FO = N
4.Medium
8 kN6 m4 m2.7 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 6 m apart, and B is 4 m above the ground and 2.7 m to the right of A. A vertical load of 8 kN acts on member AB at K, 1.08 m (horizontally) from A. Find the force FBC in member BC.

P = 8 kNL = 6 mH = 4 mhorizontal distance A to B = 2.7 mhorizontal distance A to K = 1.08 m
FBC = kN
5.Hard
w = 1.5 kN/m2 kN1 m0.5 m0.8 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.8 m below A). The beam carries a uniform load of 1.5 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 = 1.5 kN/mP = 2 kNAD = 1 mAB = 1.5 mAC = 0.8 m
FCD = kN
6.Hard
2 kN2 m0.6 m1.9 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2 m apart. The legs meet at the pin C, 2.5 m high, and are tied by the horizontal bar DE at 0.6 m. A horizontal force of 2 kN to the right acts at C. Find the tension T in the tie.

P = 2 kNAB = 2 mheight of C = 2.5 mheight of DE = 0.6 m
T = kN

Answer key

  1. 1. FCD = 44.18 kN
  2. 2. By = 7.5 kN
  3. 3. FO = 300.5 N
  4. 4. FBC = 1.867 kN
  5. 5. FCD = 7.504 kN
  6. 6. T = 1.316 kN

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