Structural Analysis, Si Edition
Structural Analysis, Si Edition
5th Edition
ISBN: 9781285051505
Author: Aslam Kassimali
Publisher: Cengage Learning
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Chapter 2, Problem 6P
To determine

Find the dead loads acting on the girder AE and beam CD.

Expert Solution & Answer
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Answer to Problem 6P

The dead load acting on the beam CD is 1082.3lb/ft_.

Dead load in Girder AE:

The dead load at C, A, and E are 13,529lb_, 4,529lb_, and 4,529lb_ respectively.

The uniformly distributed load in the girder AE is 111.3lb/ft_.

Explanation of Solution

Given information:

The thickness of the reinforced concrete slab is 4in.

The area of cross-section of the steel floor beam is Asteelbeam=18.3in.2.

The area of cross-section of the steel girder is Asteelgirder=32.7in.2.

The length, height, and thickness of the brick wall are l=25ft,h=7ft,t=6in..

Calculation:

Show the floor systemof the building as shown in Figure 1.

Structural Analysis, Si Edition, Chapter 2, Problem 6P , additional homework tip  1

Refer Figure 1.

The tributary area of the beam CD is represented by the shaded region.

Tributary area of the beam CD:

The width of the tributary area of the beam CD is B=12ft.

The width of the tributary area of the beam CD is same as the length of the beam CD. Then,

The length of the tributary area of the beam CD is 25ft.

The thickness of the concrete slab is T=4in.

Refer Table 2.1 “Unit Weights of Construction Materials” in the text book.

The unit weight of the reinforced concrete is wc=150lb/ft3.

The unit weight of the structural steel is ws=490lb/ft3.

The unit weight of the brick wall is wb=120lb/ft3.

Calculate the dead load per unit length of the beam CD as follows:

Concrete Slab:

Calculate the dead load of the concrete slab using the relation:

(DL)ConcreteSlab=L×B×H×wc (1)

Substitute 1ft for L, 12ft for B, 4in. for T, and 150lb/ft3 for wc in Equation (1).

(DL)ConcreteSlab=1ft×12ft×4in.×(1ft12in.)×150lb/ft3=600lb

Steel beam:

Calculate the dead load of the steel beam using the relation:

(DL)SteelBeam=Asteelbeam×L×ws (2)

Substitute 1ft for L, 18.3in.2 for Asteelbeam and 490lb/ft3 for ws in Equation (2).

(DL)SteelBeam=Asteelbeam×L×ws=18.3in.2×(1ft2144in.2)×1ft×490lb/ft3=62.27lb62.3lb

Calculate the dead load of the brick wall using the relation:

(DL)Brick wall=Abrick wall×L×wb=1ft×7ft×6in.×(1ft12in.)×120lb/ft3=420lb

Calculate the dead load of the beam CD as follows:

(DL)BeamCD=(DL)ConcreteSlab+(DL)SteelBeam+(DL)Brick wall=600lb+62.3lb+420lb=1082.3lb

The dead load of 1082.3lb/ft is distributed over the length of the beam CD.

Show the dead load acting on the beam as shown in Figure 2.

Structural Analysis, Si Edition, Chapter 2, Problem 6P , additional homework tip  2

Refer Figure 2.

The reaction at C and D are denoted by Cy and Dy.

The dead load on the beam is symmetrical. Then,

Cy=Dy=(1082.3lb/ft×25ft2)Cy=Dy13529lb

Show the dead load acting on the beam as shown in Figure 3.

Structural Analysis, Si Edition, Chapter 2, Problem 6P , additional homework tip  3

Refer Figure 3.

Thus, the dead load acting on the beam CD is 1082.3lb/ft_.

Show the floor system of the building as shown in Figure 4.

Structural Analysis, Si Edition, Chapter 2, Problem 6P , additional homework tip  4

Refer Figure 4.

Tributary area of the girder AE:

The width of the tributary area of the girder AE is (252)ft.

The width of the tributary area of the girder AE is same as the length of the girder AE. Then,

The length of the tributary area of the girder AE is 24ft.

The thickness of the reinforced concrete slab is T=4in.

Calculate the dead load per unit length of the girder AE as follows:

Steel beam:

Calculate the dead load of the girder AE using the relation:

(DL)SteelGirder=Asteelgirder×L×ws (3)

Substitute 1ft for L, 32.7in.2 for Asteelgirder and 490lb/ft3 for ws in Equation (3).

(DL)SteelGirder=32.7in.2×(1ft2144in.2)×1ft×490lb/ft3=111.3lb

Concentrated load at A and E.

Show the tributary area of column at A and E as shown in Figure 5.

Structural Analysis, Si Edition, Chapter 2, Problem 6P , additional homework tip  5

Refer Figure 5.

The tributary area of column at A and E are Equal.

The tributary area of column at A and E are (252)ft×6ft.

Calculate the concentrated load (P) at the column A and E the using the relation:

P=PConcret+PSteel=[(TributaryAreaofcolumn)×T×wC]+[Asteelbeam×wS×(252)]

Substitute (252)ft×6ft for TributaryAreaofcolumn, 150lb/ft3 for wc, 18.3in.2 for Asteelbeam and 490lb/ft3 for ws, and 4in. for T.

P=[150×(252)ft×6ft×4in×(1ft12in.)+18.3in.2×(1ft2144in.2)×490×(252)ft]=[3,750ft+778.38]4,529lb

Refer Figure 3.

The concentrated load at the column C is 8,279lb_.

Show the loading on the girder AE as shown in Figure 6.

Structural Analysis, Si Edition, Chapter 2, Problem 6P , additional homework tip  6

Refer Figure 6.

The reaction at A and E are denoted by Ay and Ey.

The dead load on the beam is symmetrical. Then,

Ay=Ey=(4529lb+13529lb+111.3lb/ft×24ft+4529lb2)Ay=Ey12629lb

Show the loading on the girder AE as shown in Figure 7.

Structural Analysis, Si Edition, Chapter 2, Problem 6P , additional homework tip  7

Refer Figure 7.

The dead load at C, A, and E are 13,529lb_, 4529lb_, and 4529lb_ respectively.

The uniformly distributed load in the girder AE is 111.3lb/ft_.

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