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# Please don't post this question on google D W L Problem 2 264.0mm 27.8kN/m 7.70m Determine the Maximum Shear and Bending...

Please don't post this question on google D W L Problem 2 264.0mm 27.8kN/m 7.70m Determine the Maximum Shear and Bending Stress of the Propped timber beam in the figure. The total uniform load "wt" = w+ beam weight Weight of wood is 5.6kN/m3 wt A D L
Transcribed: Please don't post this question on google D W Problem 2 264.0mm 27.8kN/m 7.70m Determine the Maximum Shear and Bending Stress of the Propped timber beam in the figure. The total uniform load "wt" = w+ beam weight Weight of wood is 5.6kN/m3 wt A D L

Given data:

Circular cross section:

wt = w+ weight of beam.

unit weight of beam = 5.6 kN/m3.

Determining propped reaction Using consistence deformation method:

assuming reaction at B is redundant.

Deflection at B.

${\left({\delta }_{B}\right)}_{p}=\frac{{w}_{t}×{L}^{4}}{8EI}$

Redundant beam:

Deflection at B.

${\left({\delta }_{B}\right)}_{R}=\frac{{R}_{B}×{L}^{3}}{3EI}$

Compatibility equations:

${\left({\delta }_{B}\right)}_{p}={\left({\delta }_{B}\right)}_{R}\phantom{\rule{0ex}{0ex}}\frac{{w}_{t}×{L}^{4}}{8EI}=\frac{{R}_{B}×{L}^{3}}{3EI}\phantom{\rule{0ex}{0ex}}{\mathbit{R}}_{\mathbf{B}}\mathbf{=}\frac{\mathbf{3}{\mathbf{w}}_{\mathbf{t}}\mathbf{L}}{\mathbf{8}}$

Determining total load on the beam:

Maximum shear and bending moment:

Zero shear location:

Maximum positive moment:

Overall maximum shear force and bending moment:

occur at support.

Moment of inertia for circular section:

Maximum bending stress:

Bending equation:

Maximum shear stress:

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