Structural Steel Design (6th Edition)
Structural Steel Design (6th Edition)
6th Edition
ISBN: 9780134589657
Author: Jack C. McCormac, Stephen F. Csernak
Publisher: PEARSON
Question
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Chapter 5, Problem 5.1PFS
To determine

(a)

The critical buckling load using Euler equation for L=4ft,d=1.5in.

Expert Solution
Check Mark

Answer to Problem 5.1PFS

30.87kips

Explanation of Solution

Given:

L=4ftd=1.5in

Calculation:

The area of a given solid round bar is

A=πd24

Substitute the d value 1.5inches.

=π ( 1.5 )24=1.77in2

Moment of inertia of solid round bar:

I=πd464putdas1.5in=π ( 1.5 )464=0.25in4

Calculating radius of gyration:

r=IA

Substitute the values of I and A in the formula:

r=IA= 0.25 1.77=0.376in

Calculate the slenderness ratio for L= 4ft:

slendernessratio=Lr=4×12in0.375in=128<200

Determine critical buckling stress:

Fc=π2×E ( L r )2whereE=elastic modulus

Substitute the values in formula:

Fc=π2×E ( L r )2=π2×29000ksi ( 128 )2=17.47ksi<36ksi

The buckling stress is less than the limit of 36 ksi. The column is in elastic range and safe.

Calculation of critical buckling load:

Pcr=Fc×A

Put in the values

Pcr=Fc×A=17.47×1.767=30.87kips

Conclusion:

Therefore, the critical buckling load is 30.87kips.

To determine

(b)

The critical buckling load using Euler equation for L=2ft9in,d=1.5in.

Expert Solution
Check Mark

Answer to Problem 5.1PFS

The buckling stress is not less than the limit of 36ksi. The column is in inelastic range. Therefore, Euler equation is not applicable.

Explanation of Solution

Given:

L=2ft9ind=1.5in

Calculation:

Calculate the slenderness ratio for L= 2ft 9in:

slendernessratio=Lr=2ft+ 9in 12ft×12in0.375in=88<200

Determine critical buckling stress:

Fc=π2×E ( L r )2whereE=elastic modulus

Substitute the values in formula:

Fc=π2×E ( L r )2=π2×29000ksi ( 88 )2=39.96ksi<36ksi

Conclusion:

The buckling stress is not less than the limit of 36ksi. The column is in inelastic range. Therefore, Euler equation is not applicable.

To determine

(c)

To find: critical buckling load using Euler equation for L=7ft6in,d=1.5in.

Expert Solution
Check Mark

Answer to Problem 5.1PFS

Euler equation is not applicable as the slenderness ratio exceeds 200.

Explanation of Solution

Given:

L=7ft6ind=1.5in

Calculation:

Calculate the slenderness ratio for L= 7ft 6in:

slendernessratio=Lr=7ft+ 6in 12ft×12in0.375in=240>200

Conclusion:

Therefore, Euler’s equation is not applicable as the slenderness ratio exceeds 200.

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