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Draw the stress distribution diagram at the base of a column of hollow circular section with external diameter 200mm and thickness 20mm. The column is 6m long having both ends fixed. It ...(contd.)

Question (contd.) carries a load of 80 kN ata n eccentricity of 25mm from the column axis. Take E = 200GPa

Subject : Structural Analysis 1

Topic : Struts

Difficulty : High

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Given data:

D=200mmd=160mmL=6mt=20mmP=80 kNeccentricity e=25mmE=200GPa=2×105MPa

To find: ExtremeStress_


Area of column, A=π4(D2d2)=π4(2002=1602)A=11309.73mm2_I=π64(D4d4)=π64(20041604)=46.36×106mmz=Iy=46.36×106100=463.6×103mm3

Since the column is fixed at both ends

Leff=L=6000mmLeff=L2=3000mm


Extreme Stresses:_

Maximum bending moment =

p.e. sec(L2PEI)

Determine the angle L2PEI

L2PEI=60002[80×1032×105×46.38×106]=0.27rad=1612sec1612=1.041


Maximum bending moment

= 80×103×25×1.041=2.08×106 Nmm_


Maximum Compresive stress

σmax=PA+MZ=80×10311309.73+2.08×1064.636×106σmax=7.52 N/mm2_σmin=PAMZ=80×10311309.732.08×1064.636×106σmin=6.62 N/mm2_

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