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 kN1 m1 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 15 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 15 kNAD = 1 mAB = 2 mAC = 0.5 m
FCD = kN
2.Easy
OAB80 NQ = ?300 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 80 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 80 NOA = 300 mmOB = 60 mm
Q = N
3.Medium
150 NQ = ?5°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 5° with the line AC. A downward force of 150 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 150 Nθ = 5°
Q = N
4.Medium
10 kN5 m1 m2.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 3.6 m high, and the horizontal tie DE is 1 m above the ground. A load of 10 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 5 mheight of C = 3.6 mheight of DE = 1 m
C = kN
5.Hard
8 kN2 kN2 m1 mABC

A uniform horizontal boom AB of weight 2 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 8 kN hangs at B. Find the magnitude of the pin reaction A.

W = 8 kNWb = 2 kNAB = 2 mAC = 1 m
A = kN
6.Hard
w = 2.5 kN/m15 kN1.5 m2.1 m1.2 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.2 m below A). The beam carries a uniform load of 2.5 kN/m over its full length and a point load of 15 kN at its free end B. Find the force FCD in the strut.

w = 2.5 kN/mP = 15 kNAD = 1.5 mAB = 3.6 mAC = 1.2 m
FCD = kN

Answer key

  1. 1. FCD = 67.08 kN
  2. 2. Q = 400 N
  3. 3. Q = 857.3 N
  4. 4. C = 6.936 kN
  5. 5. A = 18.03 kN
  6. 6. FCD = 74.92 kN

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