9. Beams Subjected to a Moment
Beams subjected to a moment are a vital consideration in structural analysis and design, as they involve the rotational forces that can significantly impact the stability and safety of various structures. A moment, often referred to as a bending moment, is the force that causes a beam to rotate about a specific axis, inducing internal stresses that must be accounted for in the design process.
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Example 1 |
A simply supported beam of span \(2.5\ m\) is subjected to a uniformly distributed load and a clockwise couple as shown in Figure 34. Draw the shear force and bending moment diagrams for the beam. \(x_2 = x_3 = 1 m\), \(W_1 = 2 kN/m\), \(W_2 = 2 kNm\). |
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Figure 34. Clockwise couple.
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Solution:
Figure 35. Clockwise couple.
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Assignment 1 |
Analyse the beam shown in Figure 36 and draw the bending moment and shear force diagrams. Locate the points of contraflexure, if any. \(x_1=x_2=2.5 m\), \(x_3=4m\), \(x_4 = 1m\), \(\theta = 30^{\circ}\), \(W_1=6.5 kN\), \(W_2=1.5 kN/m\), \(W_3 = 3 kN\) |
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Figure 36. Inclined load.
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Solution:
Please attempt this assignment. |
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Assignment 2 |
A horizontal beam \(6\ m\) long is loaded as shown in Figure 37. Draw the shear force, bending moment and thrust diagrams for the beam. \(W_1\ =\ 5 kN, \theta_1\ =\ 35^{\circ},\ x_1\ =\ 1\ m,\) \(\ W_2\ =\ 6 kN, \theta_2\ =\ 40^{\circ},\ x_2\ =\ 1.5\ m,\) \(\ W_3\ =\ 7 kN, \theta_3\ =\ 55^{\circ},\ x_3\ =\ 2\ m,\ x_4\ =\ 1.5\ m\) |
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Figure 37. Inclined load.
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Solution:
Please attempt this assignment. |
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Assignment 3 |
A horizontal beam \(x_1\ =\ 11\ m\) long is carrying a uniformly distributed load of \(W_1\ =\ 1.5\ kN / m\). The beam is supported on two supports \(x_3\ =\ 6\ m\) apart. Find the position of the supports, so that bending moment on the beam is as small as possible. Also draw the shear force and bending moment diagrams. |
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Figure 38. Simply supported beam with a distributed load.
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Solution:
Please attempt this assignment. |
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Comments (7)
Ae we doing chapters 6, 7, 8 & 9?
No. That's for Solid II.
Kindly confirm for us the formula for volumetric strain
Hello, are the notes here all we will have for SSM2 or is there a possibility for addition?
Solid Mechanics II starts from chapter 6.
Could you confirm if in example 1 the shear force diagram is correct since from my shear force calculations the forces are positive meaning the diagram ought to be upwards
Yes, in example 1, the shear force diagram is correct. There are two point loads acting downwards, which tend to shear the bar in the negative direction.