Question

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

Answer

Given data:

Civil Engineering homework question answer, step 1, image 1

Circular cross section:

D=264 mmL=7.7 mw=27.8 kN/m

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.

Civil Engineering homework question answer, step 2, image 1

Deflection at B.

δBp=wt×L48EI

Redundant beam:

Civil Engineering homework question answer, step 2, image 2

Deflection at B.

δBR=RB×L33EI

Compatibility equations:

δBp=δBRwt×L48EI=RB×L33EIRB=3wtL8

Determining total load on the beam:

wt=w+wbA=π4×0.2642=0.0547 m2wb=5.6×A kN/mwb=5.6×0.547=0.306 kN/mwt=27.8+0.306=28.106 kN/m

Beam with loading:

RB=3wtL8RB=3×28.106×7.78=81.156 kN

Civil Engineering homework question answer, step 3, image 1

Maximum shear and bending moment:

VX=-81.156+28.106XVA=135.26 kN, VB=-81.156 kNMX=81.156X-28.106X22MB=0, MA=-208.3 kN/m

Zero shear location:

0=-81.156+28.106XX=2.887 m  from B

Maximum positive moment:

Mmax=81.156×2.887-28.1062.88722Mmax=117.17 kN.m

Overall maximum shear force and bending moment:

Vmax=135.26 kNMmax=208.3 kN.m

occur at support.

Moment of inertia for circular section:

I=πd464I=π×264464=238443564.9 mm4

Maximum bending stress:

Bending equation:

MI=fyymax=d2=2642=132 mmfmax=MmaxIymaxfmax=208.3×106238443564.9×132 N/mm2fmax=115.313 N/mm2fmax=115.313 MPa

Maximum shear stress:

τmax=43τavgτavg=VmaxAτavg=135.26×103π4×2642=2.47 N/mm2τmax=43×2.47=3.29 N/mm2τmax=3.29 MPa

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