   Chapter 3, Problem 3.6.2P ### 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

# 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.

To determine

(a)

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

Explanation

Given:

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

To determine

(b)

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

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