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Steel Design (Activate Learning wi...

6th Edition
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Publisher: Cengage Learning
ISBN: 9781337094740
Chapter 3, Problem 3.6.2P
Textbook Problem
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Use A36 steel and select the lightest American Standard Channel for a tension member that will safely support a service dead load of 100 kips and a service live load of 50 kips. The member is 20 feet long, and it is connected through the web with two lines of l-inch-diameter bolts. The length of the connection is 6 inches.

a. Use LRFD.

b. Use ASD.

Expert Solution
To determine

(a)

The lightest American Standard Channel section for a tension member using the Load and Resistance Factor Design (LRFD) method.

Explanation of Solution

Given:

Dead load is 100kips.

Live load is 50kips.

Diameter of the bolt is 1in.

The yield strength (Fy) is 50ksi.

The ultimate strength (Fu) is 70ksi.

The length of the member is 20ft.

Calculation:

Write the expression for the total load acting on the section using the resistance factor as per LFRD.

TL=1.2D+1.6L      ...... (I)

Here, the total load is TL, the dead load is D and the live load is L.

Substitute 100kips for D and 50kips for L in Equation (I).

TL=(1.2×100kips)+(1.6×50kips)=120kips+80kips=200kips

The total load acting on the member is equal to the design load of the member.

TL=Pn      ...... (II)

Here, the design load is Pn.

Substitute 200kips for TL in Equation (II).

Pn=200kips

Write the expression to calculate the gross area.

Pn=0.9FyAg      ...... (III)

Here, the yield strength is Fy and the gross area is Ag.

Substitute 36ksi for Fy and 200kips for Pn in Equation (III).

200kips=0.9×(36ksi)×AgAg=200kips0.9×36ksiAg=6.173in2

Write the expression to calculate the effective area.

Pn=0.75FuAe      ...... (IV)

Here, the ultimate strength is Fu and the effective area is Ae.

Substitute 58ksi for Fu and 200kips for Pn in Equation (IV).

200kips=0.75×58ksi×AeAe=200kips0.75×58ksiAe=4.6in2

Write the expression to calculate the minimum radius of gyration.

rmin=L300      ...... (V)

Here, the length of the member is L.

Substitute 20ft for L in Equation (V).

rmin=(20ft×12in1ft)300=0

Expert Solution
To determine

(b)

The lightest American Standard Channel section for a tension member using Allowable Strength Design (ASD) method.

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Chapter 3 Solutions

Steel Design (Activate Learning with these NEW titles from Engineering!)
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