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
8 kN1.2 m0.3 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 m below A. A load of 8 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 8 kNAD = 1.2 mAB = 1.5 mAC = 0.75 m
FCD = kN
2.Easy
OAB80 NQ = ?300 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 80 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 80 NOA = 300 mmOB = 80 mm
Q = N
3.Medium
12 kN4 m2 m2.5 m1.2 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 2 m above the ground. A vertical load of 12 kN acts on leg AC at K, 1.2 m (horizontally) from A. Find the tension T in the tie.

P = 12 kNAB = 4 mheight of C = 4.5 mheight of DE = 2 mhorizontal distance A to K = 1.2 m
T = kN
4.Medium
250 NQ = ?25°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 25° with the line AC. A downward force of 250 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 250 Nθ = 25°
Q = N
5.Hard
5 kN1 kN4 m1 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 1 m above A. A load of 5 kN hangs at B. Find the tension T in the cable.

W = 5 kNWb = 1 kNAB = 4 mAC = 1 m
T = kN
6.Hard
12 kN2 kN2.5 m3 mABC

A uniform horizontal boom AB of weight 2 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 3 m above A. A load of 12 kN hangs at B. Find the tension T in the cable.

W = 12 kNWb = 2 kNAB = 2.5 mAC = 3 m
T = kN

Answer key

  1. 1. FCD = 18.87 kN
  2. 2. Q = 300 N
  3. 3. T = 2.88 kN
  4. 4. Q = 268.1 N
  5. 5. T = 22.68 kN
  6. 6. T = 16.92 kN

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