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
5 kN4.8 m2 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4.8 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 2 m. A load of 5 kN acts at C. Find the tension T in the tie DE.

P = 5 kNAB = 4.8 mheight of C = 3.6 mheight of DE = 2 m
T = kN
2.Easy
12 kN2 m1.8 m2.2 m0.75 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 12 kN acts on leg AC at the point K, 0.75 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 12 kNAB = 2 mhorizontal distance A to K = 0.75 m
By = kN
3.Medium
12 kN4.8 m1 m1 m1.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart, with its apex pin C 2 m high and the horizontal tie DE 1 m above the ground. A vertical load of 12 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the tension T in the tie.

P = 12 kNAB = 4.8 mheight of C = 2 mheight of DE = 1 mhorizontal distance A to K = 1.8 m
T = kN
4.Medium
500 NQ = ?8°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 8° with the line AC. A downward force of 500 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 500 Nθ = 8°
Q = N
5.Hard
F = ?3000 N10 mmABC

A toggle press has two equal links AB and BC, each 200 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 = 200 mmh = 10 mm
F = N
6.Hard
15 kN2 m1.8 m1.8 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 3.6 m high and the horizontal tie DE 1.8 m above the ground. A vertical load of 15 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 2 mheight of C = 3.6 mheight of DE = 1.8 mhorizontal distance A to K = 0.75 m
C = kN

Answer key

  1. 1. T = 3.75 kN
  2. 2. By = 4.5 kN
  3. 3. T = 10.8 kN
  4. 4. Q = 1779 N
  5. 5. F = 300.4 N
  6. 6. C = 6.435 kN

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