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
5 kN1.5 m1 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 m below A. A load of 5 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 5 kNAD = 1.5 mAB = 2.5 mAC = 0.6 m
FCD = kN
2.Easy
OAB250 NQ = ?180 mm50 mm

The bell crank shown turns about the pin O. A vertical force of 250 N acts at A, 180 mm from O, and is balanced by a horizontal force Q at B, 50 mm above O. Find Q.

F = 250 NOA = 180 mmOB = 50 mm
Q = N
3.Medium
10 kN8 m4 m1.2 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 4 m above the ground and 1.2 m to the right of A. A vertical load of 10 kN acts on member AB at K, 0.3 m (horizontally) from A. Find the force FBC in member BC.

P = 10 kNL = 8 mH = 4 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.3 m
FBC = kN
4.Medium
15 kN3 m1.8 m1.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 3.6 m high, and the horizontal tie DE is 1.8 m above the ground. A load of 15 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 3 mheight of C = 3.6 mheight of DE = 1.8 m
C = kN
5.Hard
5 kN3 m0.8 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 2.4 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 5 kN to the right acts at C. Find the tension T in the tie.

P = 5 kNAB = 3 mheight of C = 2.4 mheight of DE = 0.8 m
T = kN
6.Hard
20 kN6 kN5 m3 m3 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 3 m high and 3 m to the right of A. Member AB carries a vertical load of 20 kN at K, 1.2 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 20 kNQ = 6 kNL = 5 mH = 3 mhorizontal distance A to B = 3 mhorizontal distance A to K = 1.2 m
Ax = kN

Answer key

  1. 1. FCD = 22.44 kN
  2. 2. Q = 900 N
  3. 3. FBC = 0.7396 kN
  4. 4. C = 9.763 kN
  5. 5. T = 3.75 kN
  6. 6. Ax = 0.4 kN

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