5° /y' W200 x 19.3 A M = 8 kN-m E.
A couple M of moment 8 kN·m acting in a vertical plane is applied to a W200 * 19.3 rolled-steel beam as shown. Determine (a) the angle that the neutral axis forms with the horizontal plane, (b) the maxi-mum stress in the beam
Given section - W200 x 19.3 rolled steel beam
M = 8kN.m
For W200 x 19.3 rolled steel beam let us take,
I z’ = 16.66 x 10 6 mm 4 = 16.6 x 10-6m4
I y’ = 1.15 x 10 6 mm 4 = 1.15 x 10-6m4
yA = yB = - yD = -yE = (203/2) = 101.5 mm
zA = - zB = - zD = zE = (102/2) = 51 mm
Mz = (8 x 10 3) cos 45 = 7.9696 x10 3 Nm
My = -( 8 x 10 3) sin 5 = -0.6972 x 10 3 N.m
Also,
The tan Ф = Iz/ Iy tan ϴ
tan Ф = {( 16.6 x 10 -6 )/ (1.15 x 10 -6) } *tan 5
tan Ф = - 1.2629
Ф= - 51.6o
α = 51.6 – 5 = 46.6 o
σ D = {( MzyD / Iz) +( MyzD / Iy)
σ D ={ (-7.9696 x10 -3 *101.5 x 10 -3 / 16.6 x 10 -6)+( -0.6972 x 10 3* -51 x 10 -3 /1.15 x 10 6)}
σ D=79.6 x 10 6 Pa
σ D=79.6 MPa
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