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
20 kN6 m1.8 m2.7 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 6 m apart. The legs meet at the pin C, 4.5 m high, and are tied together by the horizontal bar DE at a height of 1.8 m. A load of 20 kN acts at C. Find the tension T in the tie DE.

P = 20 kNAB = 6 mheight of C = 4.5 mheight of DE = 1.8 m
T = kN
2.Easy
OAB200 NQ = ?120 mm50 mm

The bell crank shown turns about the pin O. A vertical force of 200 N acts at A, 120 mm from O, and is balanced by a horizontal force Q at B, 50 mm above O. Find Q.

F = 200 NOA = 120 mmOB = 50 mm
Q = N
3.Medium
6 kN8 m2 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 2 m above the ground and 1.2 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.3 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 8 mH = 2 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.3 m
FBC = kN
4.Medium
15 kN2 m0.4 m1 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 m below A. A load of 15 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 15 kNAD = 2 mAB = 2.4 mAC = 1 m
A = kN
5.Hard
w = 1 kN/m4 kN1.5 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 1 kN/m over its full length and a point load of 4 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 4 kNAD = 1.5 mAB = 2.5 mAC = 1.2 m
FCD = kN
6.Hard
12 kN3 kN6 m3 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 3 m high and 2.7 m to the right of A. Member AB carries a vertical load of 12 kN at K, 1.08 m (horizontally) from A, and a horizontal load of 3 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 12 kNQ = 3 kNL = 6 mH = 3 mhorizontal distance A to B = 2.7 mhorizontal distance A to K = 1.08 m
Ax = kN

Answer key

  1. 1. T = 11.11 kN
  2. 2. Q = 480 N
  3. 3. FBC = 0.7974 kN
  4. 4. A = 36.12 kN
  5. 5. FCD = 14.01 kN
  6. 6. Ax = 1.026 kN

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