05 Truss- Graphical Method

Truss: Graphical Method Theory of Structure - I

Lecture Outlines  Bow’s

Notation

 Maxwell

Diagram

 Interpretation

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of Maxwell Diagram

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Bow’s Notation  In

this system, the spaces between lines of action of the forces acting on the joints of the truss are given a lowercase letter.

 Any

force is correspondingly designated by the letters of the two spaces separated by its line of action.

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eh

ef

b

g a

c

h

f

i j

d

e

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eh

ef

b

g a

c

h

f

i j

d

e

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Maxwell’s Diagram  Maxwell

diagram is the second step while calculating the forces in truss members by Graphical Method, after Bow’s notation.

 Force

polygon is drawn first at some suitable

scale.

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b

g a

c

h

f

a

i j

b

d

e c

e

FORCE POLYGON

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d

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 After

completing the force polygon of applied forces and reactions, we will locate the intermediate points f, g, h, i, j.

 The

points will be located by drawing the lines in true sense surrounding these points.

 For

example, af and ef are drawn and where they will intersect, they will give the point f.

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b

g a

c

h

i

f

d

j e

a

i j

b h

c

f

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e

g

d

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Interpreting Maxwell Diagram  We

can find the following attributes of the truss member from the Maxwell diagram.  

Magnitude of the force Sense of the force (tension or compression)

 Length

of the line af will show the magnitude of the force in member af.

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 To

find the sense, draw FBD of joint A and read clock wise.

 Direction

of af is downward and towards the joint A means the force will be directed towards the joint.

 Force

directing towards the joint is compressive and af will be in compression.

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b B a

g

c

h

i

f

A

j

d

e a

b e f

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c

d

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 For

cross checking, take joint B and read clock wise.

 Now

it reads fa. Now fa is directing upward i.e., towards joint B, hence af or fa will be in compression.

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Example For the same truss use the Graphical Method to construct a Maxwell diagram and find the forces in the members 4 bays @ 3m

1kN

3m

2kN

2kN

2kN

1kN

45o

R1=4kN

R2=4kN

First find the reactions. Using symmetry R1 = R2 = 8/2 = 4kN

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First annotate using Bow’s Notation (label spaces between members and forces) 4 bays @ 3m

2kN

1kN

b 3m

a h

i

2kN

c j

2kN

d

k

l

m

1kN

e n

0

f

g R1=4kN

R2=4kN

First find the reactions. Using symmetry R1 = R2 = 8/2 = 4kN

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Next select a scale and draw a line representing all the loads and reactions all the loads are vertical ­ so is the line the line is the line a,b,c,d,e,f (ag, gf) ab = 1, bc = 2,...etc   ag = 4, gf = 4 begin with a zone near a reaction, e.g h ah is vertical and gh is horizontal ­ meet at g  (h & g at same point) hg is 0

i

Proceed to k in same way and half the truss is solved

4

b

3 2

k

take next zone ­ i l bi is horizontal and ih is at 45o ­ draw these lines  they meet at i Now ij is vertical and jg is horizontal. This locates j

a

jm

n

c

1

g ho 0 scale d for forces e f

Measure all lines ­ this gives the force in each member need to use a special convention to determine tension or compression

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