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
O100 N100 NQ140 mm35 mm

The handles of a pair of pliers are squeezed with 100 N each, 140 mm from the pin O, and the jaws grip a wire 35 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 100 Na = 140 mmb = 35 mm
FO = N
2.Easy
2 kN3 m0.6 m1.9 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 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 0.6 m. A load of 2 kN acts at C. Find the tension T in the tie DE.

P = 2 kNAB = 3 mheight of C = 2.5 mheight of DE = 0.6 m
T = kN
3.Medium
20 kN4.8 m1.2 m2.8 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, 4 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 20 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 4.8 mheight of C = 4 mheight of DE = 1.2 m
C = kN
4.Medium
200 NQ = ?12°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 12° with the line AC. A downward force of 200 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 200 Nθ = 12°
Q = N
5.Hard
5 kN4 kN3 m2 m1.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 2 m high and 1.8 m to the right of A. Member AB carries a vertical load of 5 kN at K, 1.08 m (horizontally) from A, and a horizontal load of 4 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 4 kNL = 3 mH = 2 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 1.08 m
Ax = kN
6.Hard
w = 1 kN/m8 kN1.6 m2.4 m1.2 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.2 m below A). The beam carries a uniform load of 1 kN/m over its full length and a point load of 8 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 8 kNAD = 1.6 mAB = 4 mAC = 1.2 m
FCD = kN

Answer key

  1. 1. FO = 500 N
  2. 2. T = 0.7895 kN
  3. 3. C = 13.17 kN
  4. 4. Q = 470.5 N
  5. 5. Ax = 1.32 kN
  6. 6. FCD = 41.67 kN

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