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Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
Publisher: Cengage Learning
ISBN: 9781337094740
BuyFind

Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
Publisher: Cengage Learning
ISBN: 9781337094740

Solutions

Chapter
Section
Chapter 10, Problem 10.4.1P
Textbook Problem

Determine the nominal flexural strength of the following welded shape: The flanges are 1 inch × 1 0  inches , the web is 3 8 inch × 45

inch , and the member is simply supported, uniformly loaded, and has continuous lateral support. A572 Grade 50 steel is used.

Expert Solution
To determine

Nominal flexural strength of the given welded shape.

Answer to Problem 10.4.1P

Mn=2.381.5×104ft-kips

Explanation of Solution

Given information:

Web thickness tw=38inch

Depth of web from inside face of flange to inside face of flange h=45in

Thickness of flange tf=1in

Area of flange Af=10in2

Calculation:

Web width to thickness ratio given by,

htw=45in38inhtw=120in

Determine web is slender or not.

5.70EFy=5.7029,00050=137.27

Now, htw<5.70EFy

From the above equation web is non slender.

Calculate the elastic section modulus by using the formula,

Sx=Ixc

Calculate Ix that is moment of inertia is given by,

Ix=112twh3+2Af(h+tf2)2Ix=112(38)(45)3+2(10)(48+12)2Ix=13430in4

Maximum distance is calculated by using the formula,

c=h2+tfc=452+1c=23.5in

Elastic section modulus about the axis Sx is calculated using the values of Ix and c,

Sx=IxcSx=1343023.5Sx=571.5in3

Tension in flange strength is given by,

Mn=FySxMn=50×571.5Mn=28575in-kips

From AISC table B4-1b than the required slenderness parameters λ and λp.

λ=bf2tfλ=102(1)λ=5λp=0.38EFfλp=0.3829,00050λp=9.152

Fcr=Fy=50ksi

Here λ<λp so the flange is compact and there is no flange local buckling.

To calculate the plate girder strength reduction factor values aw and Rpg is needed,

aw=hctwbftfaw=45(38)10(1)aw=1.688<10

From AISC Equation F5-6,

Rpg=1-aw1200+300aw(hctw-5.7EFy)1Rpg=1-1.6881200+300(1.688)(120-5.729,00050)Rpg=1.017=1.0

From AISC Equation F5-7, nominal flexural strength for the compression flange is:

Mn=RpgFcrSxMn=1×50×571.5Mn=28575×112Mn=2.381.5×104ft-kips

Conclusion:

Therefore, the nominal flexural strength for the given welded plate is 2.381.5×104ft-kips.

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