A 10 m high 150UC30 steel column is fixed at its base and restrained to move laterallyin the x direction at the top and at mid-height.Determine the allowable eccentric force P that can be applied without causing the columnto either buckle or yield. Adopt a safety factor of 2 against buckling and yielding.Hint: You may choose to use a computer program to help solve the arising iterativeequation. Alternatively, you may choose to not solve the equation at all and check thecriticality of a requirement by simple substitution. 5 m5 m100 mmd = 158 mmb= 153 mmb₁-tw2tf = 9.4 mmtw = 21.0 mmA = 3,860 mm²E = 200 GPatw₁b₁Cross section data for 150UC30d₁Ix = 17.6 x 106 mmrx = 67.5 mmIy = 5.62 × 106 mmry = 38.1 mmOy = 250 MPa

Answered: A 10 m high 150UC30 steel column is…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A 10 m high 150UC30 steel column is fixed at its base and restrained to move laterally
in the x direction at the top and at mid-height.
Determine the allowable eccentric force P that can be applied without causing the column
to either buckle or yield. Adopt a safety factor of 2 against buckling and yielding.
Hint: You may choose to use a computer program to help solve the arising iterative
equation. Alternatively, you may choose to not solve the equation at all and check the
criticality of a requirement by simple substitution.

5 m
5 m
100 mm
d = 158 mm
b= 153 mm
b₁-tw
2
tf = 9.4 mm
tw = 21.0 mm
A = 3,860 mm²
E = 200 GPa
tw
₁
b₁
Cross section data for 150UC30
d₁
Ix = 17.6 x 106 mm
rx = 67.5 mm
Iy = 5.62 × 106 mm
ry = 38.1 mm
Oy = 250 MPa

Expert Solution

Step 1: Introduction

Given Data:

A cross-section data for 150UC30 is given as:

$\begin{array}{rcl} I_{x} & = & 17.6 \times 10^{6} m m^{4} \\ I_{y} & = & 5.62 \times 10^{6} m m^{4} \\ r_{y} & = & 38.1 \\ e & = & 100 m m \\ A & = & 3860 m m^{2} \\ F . S & = & 2 \\ σ_{y} & = & 250 M P a \\ E & = & 200 \times 10^{3} M P a \\ L & = & 10 m \\ L & = & 10 \times 10^{3} m m \end{array}$

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