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
OAB400 NQ = ?120 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 400 N acts at A, 120 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 400 NOA = 120 mmOB = 60 mm
Q = N
2.Easy
12 kN4 m1.5 m1 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 2.5 m high, and are tied together by the horizontal bar DE at a height of 1.5 m. A load of 12 kN acts at C. Find the tension T in the tie DE.

P = 12 kNAB = 4 mheight of C = 2.5 mheight of DE = 1.5 m
T = kN
3.Medium
8 kN0.75 m1.25 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 8 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 8 kNAD = 0.75 mAB = 2 mAC = 1.5 m
A = kN
4.Medium
OAB120 NQ300 mm60 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 120 N at A (300 mm from O) is balanced by a horizontal force at B (60 mm above O). Find the magnitude of the pin reaction FO.

F = 120 NOA = 300 mmOB = 60 mm
FO = N
5.Hard
5 kN5 m1.5 m2.5 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 5 m apart, with its apex pin C 4 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 5 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 5 kNAB = 5 mheight of C = 4 mheight of DE = 1.5 mhorizontal distance A to K = 1.5 m
C = kN
6.Hard
F = ?4000 N20 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 20 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 4000 N at the slider C? Neglect friction and weights.

Q = 4000 NAB = BC = 150 mmh = 20 mm
F = N

Answer key

  1. 1. Q = 800 N
  2. 2. T = 12 kN
  3. 3. A = 17.07 kN
  4. 4. FO = 611.9 N
  5. 5. C = 2.121 kN
  6. 6. F = 1076 N

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