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
O80 N80 NQ = ?80 mm24 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 24 mm from the pin. Find the gripping force Q on the bolt.

F = 80 Na = 80 mmb = 24 mm
Q = N
2.Easy
3 kN1 m1.4 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 3 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 3 kNAD = 1 mAB = 2.4 mAC = 1.2 m
FCD = kN
3.Medium
OAB80 NQ300 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 80 N at A (300 mm from O) is balanced by a horizontal force at B (80 mm above O). Find the magnitude of the pin reaction FO.

F = 80 NOA = 300 mmOB = 80 mm
FO = N
4.Medium
250 NQ = ?8°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 8° 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 = 8°
Q = N
5.Hard
w = 4 kN/m2 kN0.75 m0.75 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 = 0.75 mAB = 1.5 mAC = 1 m
FCD = kN
6.Hard
2 kN1.5 kN5 m4 mABC

A uniform horizontal boom AB of weight 1.5 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 2 kN hangs at B. Find the tension T in the cable.

W = 2 kNWb = 1.5 kNAB = 5 mAC = 4 m
T = kN

Answer key

  1. 1. Q = 266.7 N
  2. 2. FCD = 9.372 kN
  3. 3. FO = 310.5 N
  4. 4. Q = 889.4 N
  5. 5. FCD = 12.5 kN
  6. 6. T = 4.402 kN

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