   Chapter 10, Problem 10.4.1P ### Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
ISBN: 9781337094740

#### Solutions

Chapter
Section ### Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
ISBN: 9781337094740
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.

To determine

Nominal flexural strength of the given welded shape.

Mn=2.381.5×104ft-kips

Explanation

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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