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------------------------------------------------ Sketch and express the section modulus of a 2x6.

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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