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8. Bending Stresses in Composite Beams

Bending stresses in composite beams play a crucial role in the performance and reliability of modern structures. As a fusion of two or more distinct materials with varying mechanical properties, composite beams offer significant advantages in terms of strength, stiffness, and weight reduction.

Idea

Example 1

In Figure 30, two wooden planks \(y_1=x_2= 150 mm \times x_1=x_2=60 mm\) each are connected to form a \(T\) section of a beam. If a moment of \(6.4 kN-m\) is applied around the horizontal neutral axis, inducing tension below the neutral axis, find the bending stresses at both the extreme fibres of the cross-section.

(i) Find the moment of inertia for the section.
(ii) Clearly show each calculation for bending stress in the upper and lower extreme fibres.

unsymmetrical-section-1
Figure 30. Unsymmetrical section.
Solution:
unsymmetrical-section-1
Figure 31. Unsymmetrical section.

Idea

Example 2

Figure 32 shows a rolled steel beam of an unsymmetrical I-section. If the maximum bending stress in the beam section is not to exceed \(45 MPa\), find the moment, which the beam can resist. \(x_1=y_2= 250 \mathrm{~mm}, x_2= 150 \mathrm{~mm}, y_1=y_3=60 \mathrm{~mm}\)

(i) Find the moment of inertia for the section.
(ii) Clearly show each calculation for moment which the beam can resist.

unsymmetrical-section-2
Figure 32. Unsymmetrical section.
Solution:
unsymmetrical-section-2
Figure 33. Unsymmetrical section.


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Comments (7)

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Brenda

Ae we doing chapters 6, 7, 8 & 9?

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Dr. Sam

No. That's for Solid II.

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Elsie

Kindly confirm for us the formula for volumetric strain

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Brenda

Hello, are the notes here all we will have for SSM2 or is there a possibility for addition?

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Dr. Sam

Solid Mechanics II starts from chapter 6.

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Robert

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

(Edited)
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Dr. Sam

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.