EGR280 Mechanics 4

8/8/2019 EGR280 Mechanics 4

1/9

EGR 280

Mechanics4 Analysis of Structures

Trusses


2/9

ANALYSIS OF STRUCTURES

No new theory!

Only new names and techniques.


3/9

TRUSS

Graphics and problem statements 2004 R.C. Hibbeler.Published by Pearson Education, Inc., Upper Saddle River, NJ.

Major engineering structure class

Composed entirely of straight, two-force members pinned at their endpoints

Loading takes place only at the joints, never between

Simple trusses are composed of basic triangular shapes


4/9

Analysis of trusses by theMethod of Joints, used to find the force in each andevery member of the truss.

Example: Determine the force in each member of the truss shown below:

Graphics and problem statements 2004R.C. Hibbeler. Published by Pearson Education, Inc.,

Upper Saddle River, NJ.

Procedure: Draw a FBD of the entire truss and determine the support reactions

Draw a FBD of each joint and write equations for the unknown member forces.

Solve the joint equations, report if each member is in tension or compression


5/9

Step 1: Determine the reaction forces on the entire truss:

Fx = Cx + 600 N = 0

Fy = Ay + Cy 400 N = 0

MC = (400 N)(3 m) Ay (6 m)

+ (600 N)(4 m) = 0

Cx = 600 N

Cy = 200 N

Ay = 600 N

A

B

C

D

Ay

400 N

Cx

Cy

600 N


6/9

Step 2: Draw a FBD of each joint, assume all members in tension, write and

solve the joint equilibrium equations

Fx = FAD + (3/5)FAB = 0

Fy = 600 N + (4/5)FAB = 0

Fx = FBC + (3/5)FBD - (3/5)FAB = 0

Fy = -400 N - (4/5)FAB - (4/5)FBD = 0

Fx

= -FBC

600 N = 0

Fy = -200 N - FCD = 0

Fx = -FAD - (3/5)FBD + 600 N = 0

Fy = FCD + (4/5)FBD = 0

A

FAB

FAD

600 N

B

400 N

FBC

FBDFAB

FBC

FCD

200 N

600 NC

600 ND

FCDFBD

FAD


7/9

Solution:

FAB = 750 N (C)

FAD = 450 N (T)

FBC = 600 N (C)

FBD = 250 N (T)

FCD = 200 N (C)




8/9

Analysis of trusses by theMethod of Sections, used to find the force in only afew members of the truss.

Example: Determine the forces in members GE, GC and BC of the trussshown



Procedure:

After finding the overall reactions, cut, or section, the truss through themembers where the forces are to be found

Draw the FBD of that part of the truss which has the fewest unknowns Write equilibrium equations to solve for the unknown forces

EXERCISE: Find the reactions Ax and Ay


9/9

Fx = FGE + (4/5)FCG + FBC 400 N = 0

Fy = 300 N (3/5)FCG = 0

MG = FBC(3 m) (400 N)(3 m) (300 N)(4 m) = 0

FGE = 800 N (C)

FGC = 500 N (T)

FBC = 800 N (T)

A

G

B

FGE

FCG

FBC

300 N

400 N

Documents

EGR280 Mechanics 4