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 = ?150 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 100 N acts at A, 150 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 100 NOA = 150 mmOB = 60 mm
Q = N
2.Easy
10 kN3.2 m1.5 m2.1 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart. The legs meet at the pin C, 3.6 m high, and are tied together by the horizontal bar DE at a height of 1.5 m. A load of 10 kN acts at C. Find the tension T in the tie DE.

P = 10 kNAB = 3.2 mheight of C = 3.6 mheight of DE = 1.5 m
T = kN
3.Medium
300 NQ = ?30°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 30° with the line AC. A downward force of 300 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 300 Nθ = 30°
Q = N
4.Medium
15 kN6 m1.2 m0.8 m1.2 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 2 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 15 kN acts on leg AC at K, 1.2 m (horizontally) from A. Find the tension T in the tie.

P = 15 kNAB = 6 mheight of C = 2 mheight of DE = 1.2 mhorizontal distance A to K = 1.2 m
T = kN
5.Hard
F = ?1000 N25 mmABC

A toggle press has two equal links AB and BC, each 80 mm long between pins. The joint B sits 25 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1000 N at the slider C? Neglect friction and weights.

Q = 1000 NAB = BC = 80 mmh = 25 mm
F = N
6.Hard
w = 1 kN/m4 kN1.6 m2.4 m0.6 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.6 m below A). The beam carries a uniform load of 1 kN/m over its full length and a point load of 4 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 4 kNAD = 1.6 mAB = 4 mAC = 0.6 m
FCD = kN

Answer key

  1. 1. Q = 250 N
  2. 2. T = 3.81 kN
  3. 3. Q = 259.8 N
  4. 4. T = 11.25 kN
  5. 5. F = 658 N
  6. 6. FCD = 42.72 kN

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