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Method of Joints Example

Using the method of joints, determine the

force in each member ofthe truss.

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Method of Joints Example

Draw the free bodydiagram of the truss and

solve for the equations

x x

x

y y

y

0

0 lb

0 2000 lb 1000 lb

3000 lb

F C

C

F E C

E C

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Method of Joints

Example

Solve the moment about C

C

y

0 2000 lb 24 ft 1000 lb 12 ft 6 ft

10000 lbC 3000 lb 10000 lb 7000 lb

M E

E

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Method of Joints

Example

Look at joint A

y AD

AD AD

x AD AB AB

AB AB

40 2000 lb

52500 lb 2500 lb C

3 30 2500 lb

5 51500 lb 1500 lb T

F F

F F

F F F F

F F

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Method of Joints

Example

Look at joint D

y AD DB DB

DB DB

x AD DB DE

DE

DE DE

4 4 4 40 2500 lb5 5 5 5

2500 lb 2500 lb T

3 30 5 5

3 32500 lb 2500 lb

5 5

3000 lb 3000 lb C

F F F F

F F

F F F F

F

F F

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Method of Joints

Example

Look at joint B

y BD BE

DE

DE DE

x BD BA BE BC

BC

BC DE

4 4

0 1000 lb5 54 4

2500 lb 1000 lb5 53750 lb 3750 lb C

3 305 5

3 32500 lb 1500 lb 3750 lb

5 5

5250 lb 5250 lb T

F F F

F

F F

F F F F F

F

F F

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Method of Joints

Example

Look at joint E

y EB EC

DE

EC EC

x EB ED EC

EC

EC EC

4 4

0 10000 lb5 54 4

3750 lb 10000 lb5 58750 lb 8750 lb C

3 305 5

3 33750 lb 3000 lb

5 5

8750 lb 8750 lb C

F F F

F

F F

F F F F

F

F F

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Method of Joints

Example

Look at joint C to check the

solution

y CE

x CE CB x

40 7000 lb

54

8750 lb 7000 lb 0 OK!5

305

38750 lb 5250 lb 0 0

5

F F

F F F C

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Method of Joints Class Problem

Determine the forces BC,

DF and GE. Using themethod of Joints.

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Method of Sections -Truss

The method of joints is most effective whenthe forces in all the members of a truss are tobe determined. If however, the force is onlyone or a few members are needed, then themethod of sections is more efficient.

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Few simple guidelines of section truss analysis :

Pass a section through a maximum of 3 members ofthe truss, 1 of which is the desired member where itis dividing the truss into 2 completely separate parts,

At 1 part of the truss, take moments about the point(at a joint) where the 2 members intersect and solvefor the member force, using M = 0,

Solve the other 2 unknowns by using the equilibriumequation for forces, using Fx = 0 and Fy = 0 .

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Method of Sections -Truss

If we were interested inthe force of member CE.We can use a cutting lineor section to breakup thetruss and solve by takingthe moment about B.

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Method of Sections Example

Determine the forces in members FH, GH and GIof the roof truss.

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Method of Sections Example

Draw a free body diagram and solve for thereactions.

RAx

RAy

L

x Ax

Ax

y

Ay

0

0 kN

0

20 kN

F R

R

F

L R

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Method ofSections Example

Solve for themoment at A.

RAx

RAy

L

A

Ay

6 kN 5 m 6 kN 10 m 6 kN 15 m

1 kN 20 m 1 kN 25 m 30 m

7.5 kN

12.5 kN

M

L

L

R

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Method of Sections Example

Solve for the member GI. Take a cut between thethird and fourth section and draw the free-bodydiagram.

HI HI

HI

1 o

8 m 10 m8 m

15 m 10 m 15 m

5.333 m

8 mtan 28.1

15 m

l l

l

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Method of Sections

Example

The free-body diagram of

the cut on the right side.

H GI

GI GI

1 kN 5 m 7.5 kN 10 m 5.333 m

13.13 kN 13.13 kN T

M F

F F

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Method of Sections Example

Use the line of action of the forces and take the momentabout G it will remove the F GI and F GH and shift F FH to the

perpendicular of G.

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Method ofSections Example

Take the moment at G

G

oFH

FH FH

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

cos 28.1 8 m

13.82 kN 13.82 kN C

M

F

F F

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Method of Sections Example

Use the line of action of the forces and take the momentabout L it will remove the F GI and F FH and shift F GH to point

G.

1 o5 mtan 133.25.333 m

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Method ofSections Example

Take the moment at L

oL GH

GH GH

1 kN 5 m 1 kN 10 m cos 43.2 15 m

1.372 kN 1.372 kN C

M F

F F

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Method of Sections Class Problem

Determine the forces in members CD and CE using method of sections.

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Homework (Due 2/24/03)

Problems:

6-34, 6-37, 6-38, 6-40, 6-45, 6-63

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Truss Bonus Problem

Determine whether themembers are unstable,

determinate orindeterminate.

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Truss Bonus Problem

Determine the loads ineach of the members.

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Truss Bonus Problem

Determine the loads ineach of the members.

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Truss Bonus Problem

Determine the loads ineach of the members.