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 kN1.5 m1.5 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 = 1.5 mAB = 3 mAC = 0.5 m
FCD = kN
2.Easy
OAB80 NQ = ?250 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 80 N acts at A, 250 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 80 NOA = 250 mmOB = 60 mm
Q = N
3.Medium
4 kN4 m1.5 m1.5 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 3 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 4 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the tension T in the tie.

P = 4 kNAB = 4 mheight of C = 3 mheight of DE = 1.5 mhorizontal distance A to K = 1.5 m
T = kN
4.Medium
12 kN2.4 m0.8 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart. The legs meet at the pin C, 2.4 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 12 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 12 kNAB = 2.4 mheight of C = 2.4 mheight of DE = 0.8 m
C = kN
5.Hard
F = ?3000 N10 mmABC

A toggle press has two equal links AB and BC, each 100 mm long between pins. The joint B sits 10 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 3000 N at the slider C? Neglect friction and weights.

Q = 3000 NAB = BC = 100 mmh = 10 mm
F = N
6.Hard
6 kN1 kN4 m1 mABC

A uniform horizontal boom AB of weight 1 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 6 kN hangs at B. Find the magnitude of the pin reaction A.

W = 6 kNWb = 1 kNAB = 4 mAC = 1 m
A = kN

Answer key

  1. 1. FCD = 94.87 kN
  2. 2. Q = 333.3 N
  3. 3. T = 2 kN
  4. 4. C = 7.5 kN
  5. 5. F = 603 N
  6. 6. A = 26 kN

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