Question

A temporary support steel frame (E 200 GPa) is made of 30-mm diameter solid circular steel rods (members AB and CD), and 22-mm diameter solid circular steel rods (members BC and AD), al pin connected at the turnbuckle corners A, B, C, and D (see Figure below). The steel frame is braced by two cables AC and BD. A turnbuckle is fitted to cable AC and tightening it will induce tension 3m in cable AC. Determine the largest allowable tension force in cable AC using a factor of safety of 2.75 with respect to buckling. (Note: you need to consider only buckling in the plane of the structure) 2.25m

Answer 1

7 turnbuckle . 3.5m A 2-25 Faom the ivor data 200 Gpa Diameter oF membr AB = 30mm Diameler ot membex CD 3om BC 23Mm Diameler Of mober AD Diameter ot membo - 2.SR Facto of, Sae Calulalion of lenath JCAB)(E AC

Ac C12.25)5.0GQS N1.3135 AC FOuce - 2EI Poee bs ciagamfo the membe at c' TAc COSO FRC TAC Sno TAC FCD heyizontal toxces o Taing BeD FBr- TAC COso e, Coo (Bc' Ac FBS -TAC. 4-1G

Tас Гвс х 1:84 - Lзтои EFy=0 "О оло, n o O2 ng Faom tuiangle Вер. FoD- TAC goo FcD -TAС 3-5 FcD X .18 - TAC . Faom equalion 1),, Fвс 1xЕх Твс (Lec п: х200 X 10' ХIBC (3-1492x 200 х1 5.OGRS

dB4 4 2214 0.T8S x 1 4641 11419.98.. --9 (314 FBC 2249- G 5.OG2S 4444.36. FBC Altocoable or ce Calculation

Pouce Allocable toRce On CD Facto o safely 2.5 AGI4.S Paom cauation TAC= Allocabie. Porce x 1-84 .GIXIOX 3.84 -- TAC FOY Ce FCD L2 E TCO (LcDj TT(200)X I0'x ICD

ТсD С т дау 4 T. dhj -хо 4- - Tх doo 4 ХIL. О-185х 50G2S 3940. G2S a o1x t tE - dг Fo x 200 X10' x 39:I4 X10 'nm+ (3-S) - (314)4200х10 o'x 39. 74- X to 12.25 183G4 1008 12.25 Foo G 41X(O N . force Allocoable Fooсе on Ср Factoo ol sakty

Q3-30 :33 X .. TeoSon î9 .tHe member Bc. TAC .33 (0 1. 18 2330 X 1-18 TAC 274(ON. Coosdcr the minimsm we have to value. ce, 3.34. x ioN