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 kN0.8 m1.7 m0.8 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.8 m below A. A load of 10 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 10 kNAD = 0.8 mAB = 2.5 mAC = 0.8 m
FCD = kN
2.Easy
6 kN4.8 m1 m1.4 m1.44 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 6 kN acts on leg AC at the point K, 1.44 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 6 kNAB = 4.8 mhorizontal distance A to K = 1.44 m
By = kN
3.Medium
400 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 400 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 400 Nθ = 15°
Q = N
4.Medium
20 kN2 m1.5 m2.5 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, 4 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 20 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 2 mheight of C = 4 mheight of DE = 1.5 m
C = kN
5.Hard
4 kN1.5 kN5 m1 mABC

A uniform horizontal boom AB of weight 1.5 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 4 kN hangs at B. Find the magnitude of the pin reaction A.

W = 4 kNWb = 1.5 kNAB = 5 mAC = 1 m
A = kN
6.Hard
w = 5 kN/m6 kN1.2 m1.2 m1.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.5 m below A). The beam carries a uniform load of 5 kN/m over its full length and a point load of 6 kN at its free end B. Find the force FCD in the strut.

w = 5 kN/mP = 6 kNAD = 1.2 mAB = 2.4 mAC = 1.5 m
FCD = kN

Answer key

  1. 1. FCD = 44.19 kN
  2. 2. By = 1.8 kN
  3. 3. Q = 746.4 N
  4. 4. C = 10.77 kN
  5. 5. A = 23.76 kN
  6. 6. FCD = 30.73 kN

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