© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Analysis of Determinate Trusses

Characteristics• Slender Members• Wooden Struts• Metal

Bars/Angles/Channels

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Analysis of Determinate Trusses

Characteristics• Pinned/Bolted

Welded Joint Connections

• Gusset Plates

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Analysis of Determinate Trusses

• Loads at Joints• Members in

Tension/Compression

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Roof Trusses - Terminology

SupportsWood/Steel/RC ColumnsMasonry Walls

Bent:Roof Truss andSupporting Columns

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Roof Trusses - Selection

Short Spans (<60 ft)Requiring Overhead Clearance

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Assumptions for Design

• Members are joined together by smooth pins– Center lines of joining members are concurrent at a point

– In reality some rigidity exists: Secondary stresses

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Assumptions for Design

• All loads are applied at joints– Self weight is neglected IF small compared to forces

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Assumptions for Design

• Axial Force Members– Tension/Compression

– Compression Members Usually Thicker

Tension

Compression

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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ition

Method of Sections

Truss in Equilibrium => Each PART in Equilibrium

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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ition

Method of Sections

Truss in Equilibrium => Each PART in Equilibrium

Efficient when forces of only a few members are to be found

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Method of Sections - Procedure

Free Body Diagram

• Determine external reactions of entire truss

• Decide how to section trussHint: Three(3) unknown forces at the most

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Method of Sections – Procedure (cont’d)

Free Body Diagram

• Draw FBD of one partHint: Choose part with least number of forces

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Method of Sections – Procedure (cont’d)

Free Body Diagram

• Establish direction of unknown forces(a)Assume all forces cause tension in member

Numerical results: (+) tension (-) compression

(a)Guess DirectionNumerical results: (+) Guess is correct (-) Force in opposite direction

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Method of Sections – Procedure (cont’d)

Equations of Equilibrium

Take moments about a point that lies on the intersection of the lines of action of two unknown forces

0

0

0

M

F

F

y

x

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Vector Mechanics for Engineers: Statics

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6 - 15

Sample Problem 6.3

Determine the force in members FH, GH, and GI.

SOLUTION:

• Take the entire truss as a free body. Apply the conditions for static equilib-rium to solve for the reactions at A and L.

• Pass a section through members FH, GH, and GI and take the right-hand section as a free body.

• Apply the conditions for static equilibrium to determine the desired member forces.

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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6 - 16

Sample Problem 6.3

SOLUTION:

• Take the entire truss as a free body. Apply the conditions for static equilib-rium to solve for the reactions at A and L.

kN 5.12

kN 200

kN 5.7

m 25kN 1m 25kN 1m 20

kN 6m 15kN 6m 10kN 6m 50

A

ALF

L

L

M

y

A

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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6 - 17

Sample Problem 6.3

• Pass a section through members FH, GH, and GI and take the right-hand section as a free body.

kN 13.13

0m 33.5m 5kN 1m 10kN 7.50

0

GI

GI

H

F

F

M

• Apply the conditions for static equilibrium to determine the desired member forces.

TFGI kN 13.13

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Vector Mechanics for Engineers: Statics

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6 - 18

Sample Problem 6.3

kN 82.13

0m 8cos

m 5kN 1m 10kN 1m 15kN 7.5

0

07.285333.0m 15

m 8tan

FH

FH

G

F

F

MGL

FG

CFFH kN 82.13

kN 371.1

0m 10cosm 5kN 1m 10kN 1

0

15.439375.0m 8

m 5tan

32

GH

GH

L

F

F

M

HI

GI

CFGH kN 371.1

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Copyright © 2010 Pearson Education South Asia Pte Ltd

Example 6.5

Determine the force in members GE, GC, and BC of the truss. Indicate whether the members are in tension or compression.

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Copyright © 2010 Pearson Education South Asia Pte Ltd

Solution

• Choose section a-a since it cuts through the three members

• Draw FBD of the entire truss

NANNAF

NDmDmNmNM

NAANF

yyy

yyA

xxx

30009001200 ;0

9000)12()3(400)8(1200 ;0

4000400 ;0

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

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Copyright © 2010 Pearson Education South Asia Pte Ltd

Solution

• Draw FBD for the section portion

)(50005

3300 ;0

)(8000)3()8(300 ;0

)(8000)3()3(400)4(300 ;0

TNFFNF

CNFmFmNM

TNFmFmNmNM

GCGCy

GEGEC

BCBCG