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.

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
5 kN2.4 m2 m2.5 m0.3 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2.4 m apart. A vertical load of 5 kN acts on leg AC at the point K, 0.3 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 5 kNAB = 2.4 mhorizontal distance A to K = 0.3 m
By = kN
2.Easy
OAB400 NQ = ?100 mm120 mm

The bell crank shown turns about the pin O. A vertical force of 400 N acts at A, 100 mm from O, and is balanced by a horizontal force Q at B, 120 mm above O. Find Q.

F = 400 NOA = 100 mmOB = 120 mm
Q = N
3.Medium
10 kN1.5 m0.9 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 10 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 10 kNAD = 1.5 mAB = 2.4 mAC = 1.5 m
A = kN
4.Medium
100 NQ = ?20°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 20° with the line AC. A downward force of 100 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 100 Nθ = 20°
Q = N
5.Hard
15 kN2.4 m1 m2.6 m0.72 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart, with its apex pin C 3.6 m high and the horizontal tie DE 1 m above the ground. A vertical load of 15 kN acts on leg AC at K, 0.72 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 2.4 mheight of C = 3.6 mheight of DE = 1 mhorizontal distance A to K = 0.72 m
C = kN
6.Hard
4 kN4.8 m1.2 m1.2 m1.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart, with its apex pin C 2.4 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 4 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 4.8 mheight of C = 2.4 mheight of DE = 1.2 mhorizontal distance A to K = 1.8 m
C = kN

Answer key

  1. 1. By = 0.625 kN
  2. 2. Q = 333.3 N
  3. 3. A = 17.09 kN
  4. 4. Q = 137.4 N
  5. 5. C = 4.956 kN
  6. 6. C = 3.354 kN

Full step-by-step solutions: practise this topic on examproblems.com.