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mh1985
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Homework Statement
A timber beam will be used to support part of the ceiling of a house. It is
going to be attached to the walls as a simply supported beam, Figure 6.
If three forces are applied to it and considering the weight of the beam as a
uniformly distributed load of magnitude w = ρAg (which you will need to
calculate and include in the FBD), determine the maximum bending stress
due to these loads.
The properties of the wooden beam are ρ = 470
kg/m^3 , σMax = 10 MPa. Can the beam support these loads or will it fail?
Homework Equations
σ = y* M / I
The Attempt at a Solution
I'm struggling to get the Moment about the axis, because of the other loads, not sure if I'm supposed to section the beam or not.
Weight of uniformly distributed load:
Not sure about this, but going by what the question gives w = ρAg
470 kg/m^3 x 0.165 m x 0.250 m x 9.81 = 190.191375 N /m
So far I have:
I = 1/12 * bh^3 = 2.1484 * 10^-4 m^4
The reactions at the bases :
I took the distributed load and put it as a resultant
ƩM @A = (RB*5 m) -(10 kN *1 m) -(5.95096 kN*2.5 m) - (10 kN * 4 m)
RB = 64.8774/5 = 12.97548 kN
Now I'm stuck as to what the next step is...