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
2 kN4.8 m0.6 m1.8 m1.2 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 2 kN acts on leg AC at the point K, 1.2 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 2 kNAB = 4.8 mhorizontal distance A to K = 1.2 m
By = kN
2.Easy
8 kN3 m1.2 m1.8 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, 3 m high, and are tied together by the horizontal bar DE at a height of 1.2 m. A load of 8 kN acts at C. Find the tension T in the tie DE.

P = 8 kNAB = 3 mheight of C = 3 mheight of DE = 1.2 m
T = kN
3.Medium
OAB120 NQ240 mm60 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 120 N at A (240 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 = 240 mmOB = 60 mm
FO = N
4.Medium
8 kN1.2 m2.8 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 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 = 1.2 mAB = 4 mAC = 0.6 m
A = kN
5.Hard
w = 1 kN/m6 kN1.5 m2.1 m0.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.5 m below A). The beam carries a uniform load of 1 kN/m over its full length and a point load of 6 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 6 kNAD = 1.5 mAB = 3.6 mAC = 0.5 m
FCD = kN
6.Hard
4 kN4 kN4 m3 m1.2 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 3 m high and 1.2 m to the right of A. Member AB carries a vertical load of 4 kN at K, 0.48 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 = 4 kNQ = 4 kNL = 4 mH = 3 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.48 m
Ax = kN

Answer key

  1. 1. By = 0.5 kN
  2. 2. T = 3.333 kN
  3. 3. FO = 494.8 N
  4. 4. A = 56.51 kN
  5. 5. FCD = 59.2 kN
  6. 6. Ax = 0.752 kN

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