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
12 kN2 m0.4 m1.2 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.2 m below A. A load of 12 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 12 kNAD = 2 mAB = 2.4 mAC = 1.2 m
FCD = kN
2.Easy
OAB50 NQ = ?150 mm120 mm

The bell crank shown turns about the pin O. A vertical force of 50 N acts at A, 150 mm from O, and is balanced by a horizontal force Q at B, 120 mm above O. Find Q.

F = 50 NOA = 150 mmOB = 120 mm
Q = N
3.Medium
OAB50 NQ200 mm60 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 50 N at A (200 mm from O) is balanced by a horizontal force at B (60 mm above O). Find the magnitude of the pin reaction FO.

F = 50 NOA = 200 mmOB = 60 mm
FO = N
4.Medium
2 kN3.2 m1 m3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart. The legs meet at the pin C, 4 m high, and the horizontal tie DE is 1 m above the ground. A load of 2 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 2 kNAB = 3.2 mheight of C = 4 mheight of DE = 1 m
C = kN
5.Hard
w = 3 kN/m6 kN1 m0.5 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 3 kN/m over its full length and a point load of 6 kN at its free end B. Find the force FCD in the strut.

w = 3 kN/mP = 6 kNAD = 1 mAB = 1.5 mAC = 0.6 m
FCD = kN
6.Hard
w = 1 kN/m12 kN1.6 m2 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 12 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 12 kNAD = 1.6 mAB = 3.6 mAC = 1.2 m
FCD = kN

Answer key

  1. 1. FCD = 27.99 kN
  2. 2. Q = 62.5 N
  3. 3. FO = 174 N
  4. 4. C = 1.133 kN
  5. 5. FCD = 24.05 kN
  6. 6. FCD = 51.75 kN

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