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
2 kN4.8 m1 m3.5 m1.44 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 2 kN acts on leg AC at the point K, 1.44 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 2 kNAB = 4.8 mhorizontal distance A to K = 1.44 m
By = kN
2.Easy
O80 N80 NQ = ?80 mm35 mm

A hand squeezes the handles of a pair of pliers with 80 N each, 80 mm from the pin O. The jaws grip a bolt 35 mm from the pin. Find the gripping force Q on the bolt.

F = 80 Na = 80 mmb = 35 mm
Q = N
3.Medium
8 kN6 m0.8 m1.6 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, 2.4 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 8 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 6 mheight of C = 2.4 mheight of DE = 0.8 m
C = kN
4.Medium
2 kN2 m2 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 2 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 2 kNAD = 2 mAB = 4 mAC = 0.5 m
A = kN
5.Hard
12 kN2.4 m0.8 m1.7 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, 2.5 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 12 kN to the right acts at C. Find the tension T in the tie.

P = 12 kNAB = 2.4 mheight of C = 2.5 mheight of DE = 0.8 m
T = kN
6.Hard
w = 4 kN/m2 kN1.2 m1.8 m1 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1 m below A). The beam carries a uniform load of 4 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 = 4 kN/mP = 2 kNAD = 1.2 mAB = 3 mAC = 1 m
FCD = kN

Answer key

  1. 1. By = 0.6 kN
  2. 2. Q = 182.9 N
  3. 3. C = 8.5 kN
  4. 4. A = 16.12 kN
  5. 5. T = 8.824 kN
  6. 6. FCD = 31.24 kN

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