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An 8 m long steel column is pinned at the top and fixed at the bottom. The column is provided with lateral support at mid-height about the weak axis. The properties of the column section are as follows: 1,= 178.1 x 10 mm ly = 18.8 x 10 mm A=8129 mm² fy=400 MPa What is the critical effective slenderness ratio? What is the Euler critical load? What is the Euler critical stress?

An 8 m long steel column is pinned at the top and fixed at the bottom. The column is provided with lateral support at mid-height about the weak axis. The properties of the column section are as follows: 1,= 178.1 x 10 mm ly = 18.8 x 10 mm A=8129 mm² fy=400 MPa What is the critical effective slenderness ratio? What is the Euler critical load? What is the Euler critical stress?

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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GUIDED PROBLEM An 8 m long steel column is pinned at the top and fixed at the bottom. The column is provided with lateral support at mid-height about the weak axis. The properties of the column section are as follows: 178.1 x 10 mm ly = 18.8 x 10 mm* A=8129 mm² fy=400 MPa What is the critical effective slenderness ratio? What is the Euler critical load? What is the Euler critical stress? a) Determine the effective lengths: a. About the x-axis: It is pinned at the top and fixed at the bottom. k=_ L =_ Effective length: b. About the y-axis: The lateral support at the mid-height will take effect. There will be two segments. Both have lengths of: One of the segments have the pinned support and the lateral support. It will be treated as pinned ends. Thus, k=. The unbraced length is L= The effective length is: kL= The other segment have the fixed support and the lateral support. It will be treated as fixed- pinned column. Thus, k =. The unbraced length is L= The effective length is: kl= From the two effective lengths, choose the larger value (since it is more critical in slenderness. Thus, the effective length for the y-axis is: Effective length: KL= kL= b) Euler Critical Load: Using E= 200 GPa for steel, the critical load based on the slenderness in the x-axis is: Now, that of the slendemess in the y-axis, c) Euler Critical Stress: Using stress = Force / Area, Pcy= n²Elx Pax=L²₂ ²Ely= L² Choose the smaller load: Perit = This is now the maximum load that the column can carry without considering buckling. (The load where the column will start to buckle) P crit ==
Transcribed Image Text:GUIDED PROBLEM An 8 m long steel column is pinned at the top and fixed at the bottom. The column is provided with lateral support at mid-height about the weak axis. The properties of the column section are as follows: 178.1 x 10 mm ly = 18.8 x 10 mm* A=8129 mm² fy=400 MPa What is the critical effective slenderness ratio? What is the Euler critical load? What is the Euler critical stress? a) Determine the effective lengths: a. About the x-axis: It is pinned at the top and fixed at the bottom. k=_ L =_ Effective length: b. About the y-axis: The lateral support at the mid-height will take effect. There will be two segments. Both have lengths of: One of the segments have the pinned support and the lateral support. It will be treated as pinned ends. Thus, k=. The unbraced length is L= The effective length is: kL= The other segment have the fixed support and the lateral support. It will be treated as fixed- pinned column. Thus, k =. The unbraced length is L= The effective length is: kl= From the two effective lengths, choose the larger value (since it is more critical in slenderness. Thus, the effective length for the y-axis is: Effective length: KL= kL= b) Euler Critical Load: Using E= 200 GPa for steel, the critical load based on the slenderness in the x-axis is: Now, that of the slendemess in the y-axis, c) Euler Critical Stress: Using stress = Force / Area, Pcy= n²Elx Pax=L²₂ ²Ely= L² Choose the smaller load: Perit = This is now the maximum load that the column can carry without considering buckling. (The load where the column will start to buckle) P crit ==
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