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
OAB100 NQ = ?100 mm75 mm

The bell crank shown turns about the pin O. A vertical force of 100 N acts at A, 100 mm from O, and is balanced by a horizontal force Q at B, 75 mm above O. Find Q.

F = 100 NOA = 100 mmOB = 75 mm
Q = N
2.Easy
8 kN1.6 m1.4 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 8 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 8 kNAD = 1.6 mAB = 3 mAC = 0.75 m
FCD = kN
3.Medium
150 NQ = ?25°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 25° 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 = 25°
Q = N
4.Medium
5 kN5 m2.5 m1.5 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 5 m apart, and B is 2.5 m above the ground and 1.5 m to the right of A. A vertical load of 5 kN acts on member AB at K, 0.9 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 5 mH = 2.5 mhorizontal distance A to B = 1.5 mhorizontal distance A to K = 0.9 m
FBC = kN
5.Hard
w = 1 kN/m12 kN1 m2 m1 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1 m below A). The beam carries a uniform load of 1 kN/m over its full length and a point load of 12 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 12 kNAD = 1 mAB = 3 mAC = 1 m
FCD = kN
6.Hard
10 kN5 m1.2 m0.8 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, 2 m high, and are tied by the horizontal bar DE at 1.2 m. A horizontal force of 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 5 mheight of C = 2 mheight of DE = 1.2 m
T = kN

Answer key

  1. 1. Q = 133.3 N
  2. 2. FCD = 35.34 kN
  3. 3. Q = 160.8 N
  4. 4. FBC = 1.548 kN
  5. 5. FCD = 57.28 kN
  6. 6. T = 12.5 kN

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