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
2 kN0.8 m1.2 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 m below A. A load of 2 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 2 kNAD = 0.8 mAB = 2 mAC = 0.75 m
FCD = kN
2.Easy
10 kN2 m0.8 m1.7 m0.5 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 10 kN acts on leg AC at the point K, 0.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 10 kNAB = 2 mhorizontal distance A to K = 0.5 m
By = kN
3.Medium
OAB150 NQ150 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 150 N at A (150 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 150 NOA = 150 mmOB = 150 mm
FO = N
4.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
5.Hard
w = 3 kN/m6 kN1.2 m1.2 m0.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.5 m below A). The beam carries a uniform load of 3 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 = 3 kN/mP = 6 kNAD = 1.2 mAB = 2.4 mAC = 0.5 m
FCD = kN
6.Hard
4 kN1.5 kN4 m2.5 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, 2.5 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 = 4 mAC = 2.5 m
A = kN

Answer key

  1. 1. FCD = 7.311 kN
  2. 2. By = 2.5 kN
  3. 3. FO = 212.1 N
  4. 4. Q = 746.4 N
  5. 5. FCD = 49.92 kN
  6. 6. A = 7.637 kN

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