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
4 kN0.6 m0.9 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 4 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 4 kNAD = 0.6 mAB = 1.5 mAC = 1 m
FCD = kN
2.Easy
O40 N40 NQ = ?80 mm24 mm

A hand squeezes the handles of a pair of pliers with 40 N each, 80 mm from the pin O. The jaws grip a bolt 24 mm from the pin. Find the gripping force Q on the bolt.

F = 40 Na = 80 mmb = 24 mm
Q = N
3.Medium
OAB50 NQ120 mm75 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 50 N at A (120 mm from O) is balanced by a horizontal force at B (75 mm above O). Find the magnitude of the pin reaction FO.

F = 50 NOA = 120 mmOB = 75 mm
FO = N
4.Medium
250 NQ = ?20°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 20° 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 = 20°
Q = N
5.Hard
5 kN1 kN5 m4 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, 4 m above A. A load of 5 kN hangs at B. Find the tension T in the cable.

W = 5 kNWb = 1 kNAB = 5 mAC = 4 m
T = kN
6.Hard
15 kN3 kN2 m2.5 mABC

A uniform horizontal boom AB of weight 3 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2.5 m above A. A load of 15 kN hangs at B. Find the tension T in the cable.

W = 15 kNWb = 3 kNAB = 2 mAC = 2.5 m
T = kN

Answer key

  1. 1. FCD = 11.66 kN
  2. 2. Q = 133.3 N
  3. 3. FO = 94.34 N
  4. 4. Q = 343.4 N
  5. 5. T = 8.804 kN
  6. 6. T = 21.13 kN

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