Question

Spacer block- Double angles L 102 x 76 X 9.5 Long legs back-to-back Problem 3 Two L102 · 76 · 9.5 structural steel angles (see below for cross-sectional properties) are used as a compression member that is 4.5 m long. The angles are separated at intervals by spacer blocks and connected by bolts (as shown), which ensure that the double-angle shape acts as a unified structural member. Assume pinned connections at each end of the column, and use E= 200 GPa for the steel. Determine the Euler buckling load for the double- angle column if the spacer block thickness is (a) 5 mm (b) 20 mm. xH STX 76 mm 76 mm ΓαΖ Spacer thickness Mass per meter Area A Designation tan a 106 103 103 106 mmº mm mm mm mm mm mm mm kg/ m 20.2 12.6 8.60 L102 x 76 x 15.9 x 76 x 9.5 x 76 x 6.4 mm 2510 1600 109 0 1 2.50 1.64 1.14 37.4 23.6 16.2 31.2 32.0 32. 3 34.8 32.3 3 1.0 mm 2 2.0 13. 9 9.59 1.19 0.787 0.554 21.5 22. 2 22.5 22.0 19.7 18.4 16.0 16.2 16.2 0.534 0.551 0.558 1

Answer 1

Page P-3 &ol" The follousing Diagtam &houes o cempesiite columm. ts 76 mm Section Propertier The section Properties fo a Standard steel 1102 X 76 X g.5 Shape are givem lim table &houes im question: Tx = li64 X lo5 mmt X= 1907 mm A - 1600 mm² -0.787 X I05 mm4 Iy (a) 5 mm S Pacer. blochthick ness :- Consider bucklimg about horizontal cros8- &etional.anes= I=2(1.64X lo5 mmt) = 3-28 X106 mmt T?(200,000 Nmm²) ( 8-28 X 10 mmt) (4500 mm)2 Pce. 12 Pcr = 319,726 N

Pape no2 Now, considet buckling about vertical crOss - lecdional oUA I 2[0.787 X 106 mmt + (5mm + 19-7 mm)(1600 m] 3.151 K106 mm4 (200,000 N/mm?) (3-151 X 106 gmmt) (4500 mm)² PcE = 307,160 N Pce %3D Euler buckling load fot 5-mnm ibacer blocks Per. 307 KN Ame. 1. (6) 20-mm sPoces. Block thick mess :- Consider buckling about iorizental cros8 -lectional axis:- Pcz - 319,I26 N (caleulated Proviouuly im Part (o)). consider buckling about sertical cross-sectional axis:- T-2[0-787X106 mmt+(20mm/t 19.7 mm C1600 mm) 106 mm4 I-4.3967 X 12(200,000 Nmm² ) (4.3967 X 10 mmt) -428,578 N Pce = EI 12 4500 mm)2 Euler Buch limg lood for 20-mm siacek blochs: Por= 320 KN