Question

Hi,

could you please provide a clear and easy to follow worked solution for the following questions. I will leave feedback that reflects the quality of your response.

The correct answers are

21.0kN.m

50.2MPa and 38.7MPa

22.6kN.m

A beam with the section illustrated in the figure below is subjected to pure bending with compressive stresses induced above the neutral axis. The beam is steel with a yield strength of 450 MPa, modulus of elasticity of 210 GPa and Poisson's ratio of 0.295. In the figure below, dimensions are given in mm. The second moment of area of the section about the centroidal z-axis illustrated is I 1.89 x 106 mm2 Determine the bending moment which would cause the entire 8 mm thick flange sections at the top and the bottom of the beam to yield Sketch the distribution of residual stress across the section if the applied moment identified in part (b) is removed Determine the maximum bending moment the bean can support if the section is in a fully plastic state y 8 Z 90 8 60 N

Answer 1

450 50MPA R.jx 10 I2-189X mmt &mm thick Cause Detesmine BM which would yjeld fOP and bottomy beam to at glaye Seehcn Nhen the beam in Jieldiny, S+xeo in the hyers the yield Stres. will greach of beam In the iure 60 M = M, Mz langes BM 70 he BM for the Web Part , Caleun g M,: = levorarm Z-82 20 distanu

M = Slayes F= Foxce in the Levor arum olisten ce Aover aum Dis M,Sex Aa) (x. GOX9) x &R 450x 6ox8x&2 /7.71R000 N-mm 7- 712 kn-m MI Calcin g MA! 32 Rh 33 Fx M2 ( xex39)) &x2x32 X 3 R85600 N-mm M2 3-285 m

MIT "2 12-712 t 3 285 21 kN.m 20.997 folly Plastic tate gecHion is the the above io yielded, when the Secion Stooo digrom - dioran giepaens the Mp X d stavn Zp Plaotic seetion modulus. A (3,+92 2 A = Abea the beam DiS faom Neutealan/ceeg ba t0th Cao UPPeu Poutio

60 A. S0 1552 mm 8x6ox2 ナH×メ& A A A,Yi A2y ! A OPPertl A2 UPa w A A2 COXBXCAHI) 3x8 x 3% Gox8 3x8 2515 32.H1 mm 552 45ox 32-413 +32 ん50x 1552x 226h003 R N-mm R2 6 b-m MP
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