(i) Strut CD is a tubular member of circular cross-section, external diameter 150mm and wall thickness 10mm. Calculate the Euler buckling force for CD. Esteel-210GPa. (Ans. 0.62MN (ii) Calculate the compressive forces acting along the axes AC and BC when CD is subjected to its buckling force. c (Ans. 0.36MM (iii) If AC and BC are solid, circular steel bars calculate their diameter such that they just experience elastic buckling unde then forces calculated in Part (ii). (Ans. 0.061r Buckling

Elements Of Electromagnetics
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A local shopping centre has its
roof supported by the structure
shown in Figure Q6. members
AC, BC and CD are slender
steel struts loaded in
compression under a total load
F in the vertical direction, equally
distributed between points A and
B. All points of load application
and the node at C are
considered to be pin-jointed and
restrained from movement
normal to the axes of the struts.
Struts AC and BC are 2m long,
while CD is 6m in length.
F/2
A
30⁰ 30⁰
C
D d
Figure Q6
F/2
B
Transcribed Image Text:A local shopping centre has its roof supported by the structure shown in Figure Q6. members AC, BC and CD are slender steel struts loaded in compression under a total load F in the vertical direction, equally distributed between points A and B. All points of load application and the node at C are considered to be pin-jointed and restrained from movement normal to the axes of the struts. Struts AC and BC are 2m long, while CD is 6m in length. F/2 A 30⁰ 30⁰ C D d Figure Q6 F/2 B
(i) Strut CD is a tubular member of circular cross-section,
external diameter 150mm and wall thickness 10mm.
Calculate the Euler buckling force for CD. Esteel-210GPa.
(Ans. 0.62MN)
(ii) Calculate the compressive forces acting along the axes of
AC and BC when CD is subjected to its buckling force.
(Ans. 0.36MN)
(iii) If AC and BC are solid, circular steel bars calculate their
diameter such that they just experience elastic buckling under
then forces calculated in Part (ii).
(Ans. 0.061m)
Buckling
(iv) The designers of the shopping centre structure decide to change the
end condition at D to fully built-in, i.e. to resist translation and rotation, and
change the strut material to aluminium alloy. Calculate the new buckling
force for CD if the cross-sectional dimensions remain as in Part (i).
Ealuminium alloy=75GPa (you may assume that L₂ = L/√2 )
(Ans. 0.44MN)
(v) If the new built-in, aluminium alloy strut, CD, is to have the same
external diameter and buckling force as the steel strut in Part (i), calculate
the required wall thickness.
(Ans. 0.016m)
6
Transcribed Image Text:(i) Strut CD is a tubular member of circular cross-section, external diameter 150mm and wall thickness 10mm. Calculate the Euler buckling force for CD. Esteel-210GPa. (Ans. 0.62MN) (ii) Calculate the compressive forces acting along the axes of AC and BC when CD is subjected to its buckling force. (Ans. 0.36MN) (iii) If AC and BC are solid, circular steel bars calculate their diameter such that they just experience elastic buckling under then forces calculated in Part (ii). (Ans. 0.061m) Buckling (iv) The designers of the shopping centre structure decide to change the end condition at D to fully built-in, i.e. to resist translation and rotation, and change the strut material to aluminium alloy. Calculate the new buckling force for CD if the cross-sectional dimensions remain as in Part (i). Ealuminium alloy=75GPa (you may assume that L₂ = L/√2 ) (Ans. 0.44MN) (v) If the new built-in, aluminium alloy strut, CD, is to have the same external diameter and buckling force as the steel strut in Part (i), calculate the required wall thickness. (Ans. 0.016m) 6
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