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
12 kN4.8 m1.2 m1.8 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 m high, and are tied together by the horizontal bar DE at a height of 1.2 m. A load of 12 kN acts at C. Find the tension T in the tie DE.

P = 12 kNAB = 4.8 mheight of C = 3 mheight of DE = 1.2 m
T = kN
2.Easy
O120 N120 NQ = ?110 mm15 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 110 mm from the pin O. The jaws grip a bolt 15 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 110 mmb = 15 mm
Q = N
3.Medium
150 NQ = ?20°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 20° 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 = 20°
Q = N
4.Medium
OAB50 NQ200 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 50 N at A (200 mm from O) is balanced by a horizontal force at B (100 mm above O). Find the magnitude of the pin reaction FO.

F = 50 NOA = 200 mmOB = 100 mm
FO = N
5.Hard
12 kN1 kN2.5 m3 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 3 m above A. A load of 12 kN hangs at B. Find the tension T in the cable.

W = 12 kNWb = 1 kNAB = 2.5 mAC = 3 m
T = kN
6.Hard
5 kN10 kN5 m4 m3 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 4 m high and 3 m to the right of A. Member AB carries a vertical load of 5 kN at K, 2.25 m (horizontally) from A, and a horizontal load of 10 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 10 kNL = 5 mH = 4 mhorizontal distance A to B = 3 mhorizontal distance A to K = 2.25 m
Ax = kN

Answer key

  1. 1. T = 8 kN
  2. 2. Q = 880 N
  3. 3. Q = 206.1 N
  4. 4. FO = 111.8 N
  5. 5. T = 16.27 kN
  6. 6. Ax = 4.875 kN

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