GUIDED PROBLEMAn 8 m long steel column is pinned at the top and fixed at the bottom. The column is providedwith lateral support at mid-height about the weak axis.The properties of the column section are as follows:178.1 x 10 mmly = 18.8 x 10 mm*A=8129 mm²fy=400 MPaWhat 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 willbe two segments. Both have lengths of:One of the segments have the pinned support and the lateral support. It will be treated aspinned 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=n²ElxPax=L²₂²Ely=L²Choose the smaller load: Perit =This is now the maximum load that the column cancarry without considering buckling. (The load where the column will start to buckle)Pcrit ==

Moment of inertia about x axis, Moment of inertia about x axis, Area of section, Yield strength, To…

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?

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

5th Edition

ISBN:9781305084766

Author:Saeed Moaveni

Publisher:Saeed Moaveni

Chapter12: Electric Current And Related Variables In Engineering

Section12.2: Electrical Circuits And Components

Problem 6BYG

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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 ==

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Step 3: (a) Determine the effective slenderness ratio.

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