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Determine the force in each member of the truss supporting a floor deck as shown in Fig. P4.29. The deck is simply supported on floor beams which, in turn, are connected to the joints of the truss. Thus, the uniformly distributed loading on the deck is transmitted by the floor beams as concentrated loads to the top joints of the truss. FIG. P4.29

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Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

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Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 4, Problem 29P
Textbook Problem
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Determine the force in each member of the truss supporting a floor deck as shown in Fig. P4.29. The deck is simply supported on floor beams which, in turn, are connected to the joints of the truss. Thus, the uniformly distributed loading on the deck is transmitted by the floor beams as concentrated loads to the top joints of the truss.

Chapter 4, Problem 29P, Determine the force in each member of the truss supporting a floor deck as shown in Fig. P4.29. The

FIG. P4.29

To determine

Find the forces in the members of the truss supporting the floor deck

Explanation of Solution

Given information:

Apply the sign conventions for calculating reactions, forces and moments using the three equations of equilibrium as shown below.

  • For summation of forces along x-direction is equal to zero (Fx=0), consider the forces acting towards right side as positive (+) and the forces acting towards left side as negative ().
  • For summation of forces along y-direction is equal to zero (Fy=0), consider the upward force as positive (+) and the downward force as negative ().
  • For summation of moment about a point is equal to zero (Matapoint=0), consider the clockwise moment as negative and the counter clockwise moment as positive.

Method of joints:

The negative value of force in any member indicates compression (C) and the positive value of force in any member indicates Tension (T).

Calculation:

Consider the forces in the member AB, BC, CD, DE, AF, FG, GH, HI, IE, BF, BG, CG, CH, DH, and DI are FAB,FBC,FCD,FDE,FAF,FFG,FGH,FHI,FIE,FBF,FBG,FCG,FCH,FDH,FDI.

Show the loading on the deck as shown in Figure 1.

Refer Figure 1.

Consider the horizontal and vertical reactions at A are Ax and Ay.

Consider the vertical reaction at E is Ey.

Calculate the value of the angle θ as follows:

tanθ=22θ=tan1(1)θ=45°

Consider the point load acting on the beam at A, B, C, D, E are denoted by PA,PB,PC,PD,PE.

Find the load acting at joint A of the truss using the relation:

PA=15kN/m×AB2=15kN/m×42m=30kN

Find the load at joint B of the truss using the relation:

PB=15kN/m×(AB+BC2)=15kN/m×(4+42)m=60kN

Find the load at joint C of the truss using the relation:

PC=15kN/m×(BC+CD2)=15kN/m×(4+42)m=60kN

Find the load at joint D of the truss using the relation:

PD=15kN/m×(CD+DE2)=15kN/m×(4+42)m=60kN

Find the load at joint E of the truss using the relation:

PE=15kN/m×(DE2)=15kN/m×(42)m=30kN

Show the load acting on the truss as shown in the Figure 2.

Refer Figure 2.

Calculate the value of the reactions at A and E as follows:

The loading on the truss is symmetrical.

Ay=Ey=30+60+60+60+302Ay=Ey=120kN

Take the sum of the forces in the horizontal direction is zero.

Fx=0Ax=0

Show the joint A as shown in Figure 3.

Refer Figure 3.

Find the forces in the members AB and AF as follows:

For Equilibrium of forces,

Fy=030FAFsin45°+120=00.707FAF=90FAF=900.707FAF=127.3kN(T)

Fx=0FAFcos45°+FAB=0FAB=127.3×0.707FAB=90kNFAB=90kN(C)

Show the joint F as shown in Figure 4.

Refer Figure 4.

Find the forces in the members FB and FG as follows:

For Equilibrium of forces,

Fy=0FFBsin45°+FFAsin45°=0FFB+FFA=0FFB=FFA

FFB=127

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Chapter 4 Solutions

Structural Analysis
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Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - Determine the force in each member of the truss...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - Determine the force in each member of the truss...Ch. 4 - 4.30 and 4.31 Determine the force in each member...Ch. 4 - 4.30 and 4.31 Determine the force in each member...Ch. 4 - Determine the forces in the top chord member GH...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.46 through 4.50 Determine the force in each...Ch. 4 - 4.46 through 4.50 Determine the force in each...Ch. 4 - 4.46 through 4.50 Determine the force in each...Ch. 4 - 4.51 through 4.55 Determine the force in each...Ch. 4 - 4.51 through 4.55 Determine the force in each...Ch. 4 - 4.51 through 4.55 Determine the force in each...Ch. 4 - 4.51 through 4.55 Determine the force in each...

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