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
15 kN3.2 m1 m3.5 m0.96 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3.2 m apart. A vertical load of 15 kN acts on leg AC at the point K, 0.96 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 15 kNAB = 3.2 mhorizontal distance A to K = 0.96 m
By = kN
2.Easy
5 kN2 m1 m1.4 m0.6 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 5 kN acts on leg AC at the point K, 0.6 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 5 kNAB = 2 mhorizontal distance A to K = 0.6 m
By = kN
3.Medium
OAB120 NQ120 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 120 N at A (120 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 120 NOA = 120 mmOB = 150 mm
FO = N
4.Medium
6 kN0.75 m1.65 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 6 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 6 kNAD = 0.75 mAB = 2.4 mAC = 1.5 m
A = kN
5.Hard
15 kN3 kN8 m4 m3.6 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 4 m high and 3.6 m to the right of A. Member AB carries a vertical load of 15 kN at K, 1.8 m (horizontally) from A, and a horizontal load of 3 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 15 kNQ = 3 kNL = 8 mH = 4 mhorizontal distance A to B = 3.6 mhorizontal distance A to K = 1.8 m
Ax = kN
6.Hard
5 kN6 m1 m1.5 m2.25 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1 m above the ground. A vertical load of 5 kN acts on leg AC at K, 2.25 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 5 kNAB = 6 mheight of C = 2.5 mheight of DE = 1 mhorizontal distance A to K = 2.25 m
C = kN

Answer key

  1. 1. By = 4.5 kN
  2. 2. By = 1.5 kN
  3. 3. FO = 153.7 N
  4. 4. A = 16.32 kN
  5. 5. Ax = 2.363 kN
  6. 6. C = 4.193 kN

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