Design Project 3 Simon AMBOISE

Buckling analysis of axially compressed columns

Case 1 : Analytical resultsCase 2 : Shell43 element presentation

Bending stressMaximum deflectionComparison with analytical results

Case 3 : Plane82 element presentation, bending stress and deflectionComparison with analytical results

Case 4 : Solid45 element, comparison with analytical resultsComparison with analytical results

Conclusion : Comparaison between these 4 cases

Presentation

Datas :Young’s Modulus: E = 2.105 MpaPoisson’s Ratio: ν = 0,3Rh = 400 MPaRe = 450 MPalength=3000 mmArea = 1800 mm²Thickness =10 mmHmax = 120 mm

Beam 189 element

2 cross-sections :

3 different measurements

t

ta

b b

a

a mm 70 95 110

b mm 120 95 80

Boundary condition:Down : FixedUp : 2 translations fixed, rotation and force’s axis allowed.

Theoretical calculations of the critical buckling load

( )2w

min2

cr

Hcr

w

min

l*kJ*E*Pcr

ss

RE*s

ils

AJi

π=

>

π=

=

= Radius of (inertia) gyration

Slenderness ratio

Critical slenderness

Critical buckling loadColumn effective length factor, forone end fixed and the other endpinned K = 0,7

T cross section : comparison

a [mm] b [mm] Jmin [mm4] i [mm] s sgr Pcr-calculated [kN] Pcr-ansys [kN]

70 120 295000 12,80191 234,3 70,24608 132,035 127,301

95 95 721562 20,02168 149,8 70,24608 322,953 310,581

110 80 979444 23,32671 128,6 70,24608 438,374 435,013

Conclution for T beam :-Variation between calculated Pcr and ANSYS Pcr < 5%-B dicreases Critical buckling load increases

T cross section : picture

L cross section : comparison

a [mm] b [mm] Jmin [mm4] i [mm] s sgr Pcr-calculated [kN] Pcr-ansys [kN]

70 120 415807,0324 15,19881 197,4 70,24608 186,105 177,973

95 95 624366 18,62445 161,1 70,24608 279,450 279,574

110 80 534585,7666 17,23346 174,1 70,24608 239,267 233,431

Conclution for L beam :-Variation between calculated Pcr and ANSYS Pcr < 5%- MaxCritical buckling load increases for b = a

JJJ

xyzzyy zzyyJJ

J 2

2

min

22+−

+=

−

T cross section : pictures

Conclusions

Higher min. moment of inertia Higher critical buckling load

Critical buckling load depend on the type of the cross section but almost its dimension.

Smaller element size : no change in result.