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
15 kN3.2 m1 m1 m0.4 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3.2 m apart. A vertical load of 15 kN acts on leg AC at the point K, 0.4 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 15 kNAB = 3.2 mhorizontal distance A to K = 0.4 m
By = kN
2.Easy
12 kN3 m1 m2 m0.9 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3 m apart. A vertical load of 12 kN acts on leg AC at the point K, 0.9 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 12 kNAB = 3 mhorizontal distance A to K = 0.9 m
By = kN
3.Medium
100 NQ = ?15°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 15° with the line AC. A downward force of 100 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 100 Nθ = 15°
Q = N
4.Medium
15 kN1 m1.5 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 m below A. A load of 15 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 15 kNAD = 1 mAB = 2.5 mAC = 0.6 m
A = kN
5.Hard
12 kN1 kN2.5 m1 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 1 m above A. A load of 12 kN hangs at B. Find the magnitude of the pin reaction A.

W = 12 kNWb = 1 kNAB = 2.5 mAC = 1 m
A = kN
6.Hard
10 kN1.5 kN6 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 10 kN hangs at B. Find the tension T in the cable.

W = 10 kNWb = 1.5 kNAB = 6 mAC = 4 m
T = kN

Answer key

  1. 1. By = 1.875 kN
  2. 2. By = 3.6 kN
  3. 3. Q = 186.6 N
  4. 4. A = 66.43 kN
  5. 5. A = 31.25 kN
  6. 6. T = 19.38 kN

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