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LIVE LOAD ON INCLINED ON INCLINED ROOF

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CLARIFICATION PLEASE:

I HAVE A CLEAR SPAN OF 56 M BUILDING FOR WHICH ROOF IS INCLINED AT A SLOPE OF 33 DEGREES WITH INCLINED ROOF RAFTERS 1 AND 2

I HAVE APPLIED DEAD LOAD AND LIVE LOAD ON INCLINED ROOF AS FOLLOWS

LOAD CASE 1 DEAD LOAD 

MEMBER LOAD 

1 2 UNI GY 1.5

LOAD CASE 2 LIVE LOAD 

MEMBER LOAD

1 2 UNI GY 3.5

I FIND THE REACTIONS AS FOLLOWS

TOTAL DEAD LOAD REACTION= 84

TOTAL LIVE LOAD REACTION=233.7

AS PER DEAD LOAD REACTION UNIFORM DEAD LOAD IS APPLIED ON HORIZONTAL  PROJECTION=56 X 1.5=84

HOWEVER SAME WAY REACTION FOR LIVE LOAD SHOULD HAVE BEEN=56 X 3.5=196. BUT IT SEEMS IT HAS CONSIDERED INCLINED LENGTH WHICH IS 56/COS(33).

WHY IT HAS CONSIDERED INCLINED LENGTH AS THE LOAD IS APPLIED GLOBAL Y AXIS DIRECTION AND LIVE LOAD IS APPLIED ALWAYS ON HORIZONTAL PROJECTION?

PLEASE CLARIFY.


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