Question 2 [10] A simply supported wooden beam with a rectangular cross section (as shown in the figure) spans a length L and is oriented such that its longitudinal axis lies horizontally. The cross section is inclined at an angle $\alpha$ from the horizontal. The beam is subjected to a uniformly distributed vertical load of intensity q, applied through the centroid C of the section. The following data is provided: b= 150 mm; h= 200 mm; L = 2 m; $\alpha$ = 27°; q = 22 kN/m. Determine the orientation of the neutral axis under the applied loading and the maximum tensile stress developed in the beam. y C q h Figure: Q2 $\alpha$
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Given: - Beam type: Simply supported - Cross-section: Rectangular - Width, b = 150 mm = 0.150 m - Height, h = 200 mm = 0.200 m - Span length, L = 2 m - Inclination angle, $\alpha$ = 27° - Distributed vertical load, q = 22 kN/m = 22000 N/m Show more…
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$6.4-2$ A wood beam of rectangular cross section (see figure $)$ is simply supported on a span of length $L .$ The longitudinal axis of the beam is horizontal, and the cross section is tilted at an angle $\alpha .$ The load on the beam is a vertical uniform load of intensity $q$ acting through the centroid $C$ Determine the orientation of the neutral axis and calculate the maximum tensile stress $\sigma_{\max }$ if $b=80 \mathrm{mm}$ \[ h=140 \mathrm{mm}, L=1.75 \mathrm{m}, \alpha=22.5^{\circ}, \text { and } q=7.5 \mathrm{kN} / \mathrm{m} \]
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A wood beam with a rectangular cross section (see figure) is simply supported on a span of length $L$. The longitudinal axis of the beam is horizontal, and the cross section is tilted at an angle $\alpha$ The load on the beam is a vertical uniform load of intensity $q$ acting through the centroid $C$ Determine the orientation of the neutral axis and calculate the maximum tensile stress $\sigma_{\max }$ if \[ \begin{array}{l} b=80 \mathrm{mm}, h=140 \mathrm{mm}, L=1.75 \mathrm{m}, \alpha=22.5^{\circ}, \text { and } \\ q=7.5 \mathrm{kN} / \mathrm{m} \end{array} \]
A wood cantilever beam with a rectangular cross section and length $L$ supports an inclined load $P$ at its free end (see figure) Determine the orientation of the neutral axis and calculate the maximum tensile stress $\sigma_{\max }$ due to the load $P .$ Data for the beam are $b=80 \mathrm{mm}$ \[ h=140 \mathrm{mm}, L=2.0 \mathrm{m}, P=575 \mathrm{N}, \text { and } \alpha=30^{\circ} \]
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