SFD and BMD in Frames

7/26/2019 SFD and BMD in Frames

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EAS253: THEORY OF STRUCTURES


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Internal forces on section of a frame


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Solution


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Solution


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Solution


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Solution


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Solution


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Direction of action of Q, S and M

Direction of action is defined withrespect to section perpendicular

to axis of member


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Direction of action is defined withrespect to section perpendicular

to axis of member


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Member BC

01010152

5

x

xxM

1001552 2 xx.M

mx 100


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'Bx

'B

'B

100

'BB'B xvv 5

'Bx515

mx 'B 3

5.122


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5.122

100


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5.122

100


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Where to draw the SF and BM ?

BM: drawn on compression side

5.122100


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Sign convention of Q, S, MAxis for plotting

of Q, S and M



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Sign convention of Q, S, MAxis for plotting

of Q, S and M



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Axis for plotting of Q, S and M



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Sign convention of Q, S, M


FBD to the left of

the cut section


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Sign convention of Q, S, M


and deformed shape corresponding to positive M


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:0YF

Member AB

Q

15kN

kNQ 15

Member BC

15kN

10kN

10kN

Q

:0XF

0Q

Member CD

Q

35kN

:0YF

kNQ 35

A -15

D-35

Axial force diagram (thrust

diagram)(kN)

A

A

D

x

y


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7m


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Solution


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7m


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-


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-


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BC:

AB:

C

A

B C


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-


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Solution


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Bending moment diagram(kNm)

Shear force diagram(kN)


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EAS253 THEORY OF STRUCTURES


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Q

BC:

AB:

mx 50



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BC:



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Two different ways of drawing BMD



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About SFD and BMD on problems which are symmetry

P

P/2

-P/2SFD

PL/4

L/2 L/2

BMD

1



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P

P/2

-P/2SFD

PL/4

L/2 L/2

BMD

2

positive

negative



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w

1



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w

12



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About AFD(Axial Force Diagram) on problems which are symmetry

Q2 Q2 Q2

Q1Q1Q1



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Solution

AY

EY



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other



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- Member BC (=member DC)



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3

45



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x

x

5

4

x

5

3



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Complete SFD obtained by

consideration of symmetry



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Complete SFD obtained by




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Complete BMD obtained by




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BC:

AB:



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sign of curvature(=sign of

bending moment changes)



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BMD drawn using two different ways : drawn on compression side

and drawn on tension side



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BMD drawn using two different ways : drawn on compression side and

drawn on tension side



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BMD drawn using two different ways : drawn on compression side and

drawn on tension side



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SFD and BMD in Frames

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