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
10 kN2 m1 m2 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2 m apart. The legs meet at the pin C, 3 m high, and are tied together by the horizontal bar DE at a height of 1 m. A load of 10 kN acts at C. Find the tension T in the tie DE.

P = 10 kNAB = 2 mheight of C = 3 mheight of DE = 1 m
T = kN
2.Easy
15 kN6 m0.8 m3.2 m1.5 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 6 m apart. A vertical load of 15 kN acts on leg AC at the point K, 1.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 15 kNAB = 6 mhorizontal distance A to K = 1.5 m
By = kN
3.Medium
200 NQ = ?30°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 30° with the line AC. A downward force of 200 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 200 Nθ = 30°
Q = N
4.Medium
12 kN1.2 m0.3 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 12 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 12 kNAD = 1.2 mAB = 1.5 mAC = 1.5 m
A = kN
5.Hard
10 kN1 kN3 m2 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, 2 m above A. A load of 10 kN hangs at B. Find the tension T in the cable.

W = 10 kNWb = 1 kNAB = 3 mAC = 2 m
T = kN
6.Hard
12 kN3 kN5 m1 mABC

A uniform horizontal boom AB of weight 3 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 = 3 kNAB = 5 mAC = 1 m
A = kN

Answer key

  1. 1. T = 2.5 kN
  2. 2. By = 3.75 kN
  3. 3. Q = 173.2 N
  4. 4. A = 12.37 kN
  5. 5. T = 18.93 kN
  6. 6. A = 67.52 kN

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