Answer :
The section modulus (S) is a property used in structural engineering to characterize the strength and stiffness of a beam's cross-sectional shape. It is denoted by the symbol "S" and is calculated using the formula:
[tex]\[ S = \dfrac{b \times d^2}{6} \][/tex]
where:
- [tex]\( b \)[/tex] is the width of the beam's cross-section.
- [tex]\( d \)[/tex] is the distance from the neutral axis to the outermost fibers.
For a 2x6 beam, the dimensions are as follows:
- [tex]\( b \)[/tex] (width) = 1.5 inches (the actual width of a 2x6, which is nominal 2 inches).
- [tex]\( d \)[/tex] (depth) = 5.5 inches (the actual depth of a 2x6).
[tex]\[ S = \dfrac{(1.5) \times (5.5)^2}{6} \][/tex]
[tex]\[ S = \dfrac{1.5 \times 30.25}{6} \][/tex]
[tex]\[ S = \dfrac{45.375}{6} \][/tex]
[tex]\[ S = 7.5625 \, \text{in}^3 \][/tex]
So, the section modulus of a 2x6 beam is [tex]\( 7.5625 \, \text{in}^3 \)[/tex].
(Given in attachment)
Please note that the above calculations assume a simple rectangular cross-section, and actual values may vary based on factors such as wood species and any modifications to the beam's geometry.
Final answer:
The section modulus is a measure of strength and stiffness of a structural member. 2-2x6 refers to a beam made up of two 2x6 lumber pieces. The section modulus can be calculated using the formula Z = (b * h^2) / 6.
Explanation:
The section modulus is a property used in engineering to measure the strength and stiffness of a structural member. For a given shape, the section modulus indicates the resistance of the member to bending.
In this case, the section modulus of 2-2x6 refers to a beam with a cross-section that consists of two 2x6 dimensional lumber pieces. To sketch this cross-section, you would draw two rectangles representing the 2x6 lumber pieces placed horizontally next to each other. The section modulus value can be calculated using the formula: Z = (b * h^2) / 6, where b is the width of the rectangle and h is the height.
For example, if the width (b) of the 2x6 lumber is 2 inches and the height (h) is 6 inches, the section modulus would be Z = (2 * 6^2) / 6 = 24 cubic inches.
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