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
8 kN4.8 m1.8 m2.7 m1.44 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 8 kN acts on leg AC at the point K, 1.44 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 8 kNAB = 4.8 mhorizontal distance A to K = 1.44 m
By = kN
2.Easy
OAB150 NQ = ?100 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 150 N acts at A, 100 mm from O, and is balanced by a horizontal force Q at B, 150 mm above O. Find Q.

F = 150 NOA = 100 mmOB = 150 mm
Q = N
3.Medium
OAB250 NQ120 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 250 N at A (120 mm from O) is balanced by a horizontal force at B (100 mm above O). Find the magnitude of the pin reaction FO.

F = 250 NOA = 120 mmOB = 100 mm
FO = N
4.Medium
8 kN4.8 m0.8 m1.7 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, 2.5 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 8 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 4.8 mheight of C = 2.5 mheight of DE = 0.8 m
C = kN
5.Hard
w = 5 kN/m3 kN1.5 m1.5 m1.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.5 m below A). The beam carries a uniform load of 5 kN/m over its full length and a point load of 3 kN at its free end B. Find the force FCD in the strut.

w = 5 kN/mP = 3 kNAD = 1.5 mAB = 3 mAC = 1.5 m
FCD = kN
6.Hard
w = 2 kN/m6 kN1 m1.5 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 2 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 = 2 kN/mP = 6 kNAD = 1 mAB = 2.5 mAC = 0.5 m
FCD = kN

Answer key

  1. 1. By = 2.4 kN
  2. 2. Q = 100 N
  3. 3. FO = 390.5 N
  4. 4. C = 6.92 kN
  5. 5. FCD = 29.7 kN
  6. 6. FCD = 47.52 kN

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