What is the relationship between slope and bending moment in a penstock beam?

[Zohra]

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Hi ,
Please I have to understand the solution of an exercice about calculating bending moment in penstock :
It is assumed that maximum moment from penstock beam bending occurs at supports.
The bending moment M is approximated by the formula : M =w * L² /9
where w = unit load (lb/ft) and L span (ft)

w in my case is the total weight = 13 205 lb/lin ft and L=100 ft so easily i did M= 13 205 * 100² /9 =...
but in the solution i find M = (13 205 / cos(8.306) *100 /9 !
cos(8.306) is the penstock slope
Can you please explain me why divise by the slope ? I thank you so much
Zohra

 

[PhanthomJay]

Is L the horizontal distance between supports or is it measured along the slope?

 

[Zohra]

Is L the horizontal distance between supports or is it measured along the slope?

Thank you very much for your answer .
L is the horizontal distance between supports.

 

[PhanthomJay]

Thank you very much for your answer .
L is the horizontal distance between supports.

Okay. Thus, the beam is longer than L. Use the sloping direction as the x-x axis. What value should you then use for the portion of the uniform load that causes bending?

 

[Zohra]

Okay. Thus, the beam is longer than L. Use the sloping direction as the x-x axis. What value should you then use for the portion of the uniform load that causes bending?

Thank you very much
Please , by "lin ft " it means horizontal foot or foot along the slope ?

 

[PhanthomJay]

Please , by "lin ft " it means horizontal foot or foot along the slope ?

weight is distributed along the beam itself, along the slope

 

[Zohra]

weight is distributed along the beam itself, along the slope

Understood Thank you very much for your great help