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

P = 6 kNAD = 1.6 mAB = 2 mAC = 0.8 m
FCD = kN
2.Easy
O120 N120 NQ150 mm30 mm

The handles of a pair of pliers are squeezed with 120 N each, 150 mm from the pin O, and the jaws grip a wire 30 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 120 Na = 150 mmb = 30 mm
FO = N
3.Medium
10 kN0.6 m1.4 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 10 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 10 kNAD = 0.6 mAB = 2 mAC = 1.5 m
A = kN
4.Medium
6 kN3 m1 m2 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3 m apart, with its apex pin C 3 m high and the horizontal tie DE 1 m above the ground. A vertical load of 6 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the tension T in the tie.

P = 6 kNAB = 3 mheight of C = 3 mheight of DE = 1 mhorizontal distance A to K = 0.75 m
T = kN
5.Hard
5 kN6 m1.2 m1.2 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 are tied by the horizontal bar DE at 1.2 m. A horizontal force of 5 kN to the right acts at C. Find the tension T in the tie.

P = 5 kNAB = 6 mheight of C = 2.4 mheight of DE = 1.2 m
T = kN
6.Hard
w = 2 kN/m15 kN1.5 m0.9 m0.6 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.6 m below A). The beam carries a uniform load of 2 kN/m over its full length and a point load of 15 kN at its free end B. Find the force FCD in the strut.

w = 2 kN/mP = 15 kNAD = 1.5 mAB = 2.4 mAC = 0.6 m
FCD = kN

Answer key

  1. 1. FCD = 16.77 kN
  2. 2. FO = 720 N
  3. 3. A = 26.87 kN
  4. 4. T = 1.125 kN
  5. 5. T = 5 kN
  6. 6. FCD = 74.96 kN

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