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 kN3 m0.6 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, 2.4 m high, and are tied together by the horizontal bar DE at a height of 0.6 m. A load of 8 kN acts at C. Find the tension T in the tie DE.

P = 8 kNAB = 3 mheight of C = 2.4 mheight of DE = 0.6 m
T = kN
2.Easy
6 kN2 m1.5 m1.5 m0.25 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 6 kN acts on leg AC at the point K, 0.25 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 6 kNAB = 2 mhorizontal distance A to K = 0.25 m
By = kN
3.Medium
OAB250 NQ120 mm80 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 (80 mm above O). Find the magnitude of the pin reaction FO.

F = 250 NOA = 120 mmOB = 80 mm
FO = N
4.Medium
300 NQ = ?15°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 15° with the line AC. A downward force of 300 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 300 Nθ = 15°
Q = N
5.Hard
6 kN8 kN5 m2 m2.25 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 2 m high and 2.25 m to the right of A. Member AB carries a vertical load of 6 kN at K, 1.688 m (horizontally) from A, and a horizontal load of 8 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 6 kNQ = 8 kNL = 5 mH = 2 mhorizontal distance A to B = 2.25 mhorizontal distance A to K = 1.688 m
Ax = kN
6.Hard
8 kN5 m1.5 m2.1 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 3.6 m high, and are tied by the horizontal bar DE at 1.5 m. A horizontal force of 8 kN to the right acts at C. Find the tension T in the tie.

P = 8 kNAB = 5 mheight of C = 3.6 mheight of DE = 1.5 m
T = kN

Answer key

  1. 1. T = 3.333 kN
  2. 2. By = 0.75 kN
  3. 3. FO = 450.7 N
  4. 4. Q = 559.8 N
  5. 5. Ax = 0.8156 kN
  6. 6. T = 6.857 kN

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