Steel Design (Activate Learning with these NEW titles from Engineering!)
Steel Design (Activate Learning with these NEW titles from Engineering!)
6th Edition
ISBN: 9781337094740
Author: Segui, William T.
Publisher: Cengage Learning
Question
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Chapter 4, Problem 4.7.10P
To determine

(a)

Axial Compressive design strength of column AB.

Expert Solution
Check Mark

Answer to Problem 4.7.10P

728kips

Explanation of Solution

Calculation:

calculate the ratio of column stiffness to girder at each and column AB by using the equation.

GA=ICLCIgLg

Here we have

G=ratio of column stiffness to girder stiffness

IC =Moment of inertia of column

Lg =Moment of inertia of girder

LC =Length of column

Lg =Length of column

GB=10

Here ratio of column stiffness to girder stiffness at end A is GA

For Joint A:

GA=ICLCIgLg

Substitute

IgLg=(80018+80020),IC=597,LC=15

GA=ICLCIgLg    =(59715)(80018+80020)     =0.471

Refer the alignment chart for the value of Kx=1.78

Calculate the effective slenderness ratio for column by using the equation

Here Kx is the effective length factor in X direction, rx is the radius of gyration in X direction, L is the length of the member between the supports

Effective slenderness ratio=KxLrx                                          =1.78(15×12)5.31                                          =60.34

Calculate the upper limit elasticity using the equation

Upper limit elasticity=4.71EFy                                 =4.712900050                                 =113.4

Since 60.34 is less than 113.34, the column is elastic

Calculate the factored load by LRFD by using the equation

Pu=1.2D+1.6L

He re D is the dead load, L is the live load

Substitute

D=50,L=150

Pu=1.2D+1.6L     =1.2(50)+1.6(150)     =300kips

Calculate the stress coming on the column

Stress=PuAgSubstitute Pu=300,Ag=21.1

Stress=PuAg         =30021.1         =14.22ksi

Refer table 421 form AISC steel manual τb=1.00

No modification is necessary

Calculate effective slenderness ratio in y direction

Effective slenderness ratio=KyLrySubstitute k=1.0,L=15ft,ry=3.04slenderness ratio=KyLry                          =1(15×12)883.04                          =59.21<60.34

Calculate the buckling stress using the formula.

Fe=π2E(KL/r)2Substitute E=29000,KL/r=60.34Fe=π2E(KL/r)2    =π22900060.342    =78.61ksi

Check for slenderness ratio by using the formula.

Slenderness ratio=4.71EFy

Here Fy is the yield strength

Fy=50ksi,E=29000

Slenderness ratio=4.712900050                           =113.4

Since 60.34 is less than 113.4, so calculate the buckling stress using the formula

Fcr=0.658(FyFe)Fy      =0.658(5078.61)(50)      =38.31ksi

Calculate the nominal compressive strength of column.

Pn=FcrAgHere we have Ag=21.1,Fcr=38.31,Pn=FcrAg    =38.31(21.1)    =808.3kipsCalculate the design strength of the column by LRFD method.

Pu=ϕPn     =0.9(808.3)     =728kips

Conclusion:

Hence, here the design strength is estimated using the formula: Pu=ϕP

ii.

To determine

Themaximum axial compressive strength of column AB.

ii.

Expert Solution
Check Mark

Answer to Problem 4.7.10P

484kips

Explanation of Solution

Calculation:

Calculate the factored load by ASD by using the equation

Pa=D+L

He re D is the dead load L is the live load

Substitute

D=50,L=150

Pa=D+L     =50+150     =200kips

Calculate stress coming on column.

Stress=PuAgPu=200,Ag=21.1Stress=PuAg         =20021.1         =9.47ksi

Refer table 421 form AISC steel manual τb=1

No modification is necessary

Calculate effective slenderness ratio in y direction

Effective slenderness ratio=KyLry

K=1.0,L=15ft,ry=3.04

slenderness ratio=KyLry                          =1(15×12)883.04                          =59.21<60.34

Calculate the buckling stress using the formula

Fe=π2E(KL/r)2Substitute E=29000,KL/r=60.34Fe=π2E(KL/r)2    =π22900060.342    =78.61ksi

Check for slenderness ratio by using the formula.

Slenderness ratio=4.71EFy

Here Fy is the yield strength.

Fy=50ksi,E=29000

Slenderness ratio=4.712900050                           =113.4

Since 60.34 is less than 113.4, so calculate the buckling stress using the formula.

Fcr=0.658(FyFe)Fy      =0.658(5078.61)(50)      =38.31ksi

Calculate the compressive strength of column.

Pn=FcrAgHere we have ,Ag=21.1,Fcr=38.31Pn=FcrAg    =38.31(21.1)    =808.3kips

Calculate the maximum strength by using the formula.

 Maximum  strength=PnΩ                              =808.31.67                             =484kips

Conclusion:

Therefore, the maximum strength is calculated using the formula:  Maximum  strength=PnΩ                             

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