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1/98

EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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4/98

EAS253: THEORY OF STRUCTURES

Internal forces on section of a frame

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EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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7/98

EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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9/98

EAS253: THEORY OF STRUCTURES

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10/98

EAS253: THEORY OF STRUCTURES

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11/98

EAS253: THEORY OF STRUCTURES

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12/98

EAS253: THEORY OF STRUCTURES

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13/98

EAS253: THEORY OF STRUCTURES

Solution

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EAS253: THEORY OF STRUCTURES

Solution

7/26/2019 SFD and BMD in Frames

15/98

EAS253: THEORY OF STRUCTURES

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16/98

EAS253: THEORY OF STRUCTURES

Solution

7/26/2019 SFD and BMD in Frames

17/98

EAS253: THEORY OF STRUCTURES

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18/98

EAS253: THEORY OF STRUCTURES

Solution

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19/98

EAS253: THEORY OF STRUCTURES

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20/98

EAS253: THEORY OF STRUCTURES

Solution

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EAS253: THEORY OF STRUCTURES

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22/98

EAS253: THEORY OF STRUCTURES

Direction of action of Q, S and M

Direction of action is defined withrespect to section perpendicular

to axis of member

7/26/2019 SFD and BMD in Frames

23/98

EAS253: THEORY OF STRUCTURES

Direction of action is defined withrespect to section perpendicular

to axis of member

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24/98

EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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27/98

EAS253: THEORY OF STRUCTURES

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28/98

EAS253: THEORY OF STRUCTURES

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29/98

EAS253: THEORY OF STRUCTURES

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30/98

EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

Member BC

01010152

5

x

xxM

1001552 2 xx.M

mx 100

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EAS253: THEORY OF STRUCTURES

'Bx

'B

'B

100

'BB'B xvv 5

'Bx515

mx 'B 3

5.122

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EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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36/98

EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

5.122

100

7/26/2019 SFD and BMD in Frames

39/98

EAS253: THEORY OF STRUCTURES

5.122

100

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40/98

EAS253: THEORY OF STRUCTURES

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EAS253: THEORY OF STRUCTURES

Where to draw the SF and BM ?

BM: drawn on compression side

5.122100

7/26/2019 SFD and BMD in Frames

42/98

Sign convention of Q, S, MAxis for plotting

of Q, S and M

EAS253: THEORY OF STRUCTURES

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43/98

Sign convention of Q, S, MAxis for plotting

of Q, S and M

EAS253: THEORY OF STRUCTURES

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Axis for plotting of Q, S and M

EAS253: THEORY OF STRUCTURES

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Sign convention of Q, S, M

EAS253: THEORY OF STRUCTURES

FBD to the left of

the cut section

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46/98

Sign convention of Q, S, M

EAS253: THEORY OF STRUCTURES

and deformed shape corresponding to positive M

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EAS253: THEORY OF STRUCTURES

: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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48/98

EAS253: THEORY OF STRUCTURES

7m

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EAS253: THEORY OF STRUCTURES

Solution

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EAS253: THEORY OF STRUCTURES

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51/98

EAS253: THEORY OF STRUCTURES

7m

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52/98

EAS253: THEORY OF STRUCTURES

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53/98

EAS253: THEORY OF STRUCTURES

-

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54/98

EAS253: THEORY OF STRUCTURES

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55/98

EAS253: THEORY OF STRUCTURES

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56/98

EAS253: THEORY OF STRUCTURES

-

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57/98

EAS253: THEORY OF STRUCTURES

BC:

AB:

C

A

B C

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EAS253: THEORY OF STRUCTURES

-

7/26/2019 SFD and BMD in Frames

59/98

EAS253: THEORY OF STRUCTURES

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60/98

EAS253: THEORY OF STRUCTURES

Solution

7/26/2019 SFD and BMD in Frames

61/98

EAS253: THEORY OF STRUCTURES

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62/98

EAS253: THEORY OF STRUCTURES

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63/98

EAS253: THEORY OF STRUCTURES

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64/98

EAS253: THEORY OF STRUCTURES

Bending moment diagram(kNm)

Shear force diagram(kN)

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65/98

EAS253: THEORY OF STRUCTURES

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66/98

EAS253: THEORY OF STRUCTURES

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67/98

EAS253: THEORY OF STRUCTURES

EAS253 THEORY OF STRUCTURES

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68/98

EAS253: THEORY OF STRUCTURES

Q

BC:

AB:

mx 50

EAS253 THEORY OF STRUCTURES

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69/98

EAS253: THEORY OF STRUCTURES

BC:

EAS253 THEORY OF STRUCTURES

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70/98

EAS253: THEORY OF STRUCTURES

Two different ways of drawing BMD

EAS253 THEORY OF STRUCTURES

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71/98

EAS253: THEORY OF STRUCTURES

EAS253 THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

72/98

EAS253: THEORY OF STRUCTURES

About SFD and BMD on problems which are symmetry

P

P/2

-P/2SFD

PL/4

L/2 L/2

BMD

1

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

73/98

EAS253: THEORY OF STRUCTURES

About SFD and BMD on problems which are symmetry

P

P/2

-P/2SFD

PL/4

L/2 L/2

BMD

2

positive

negative

EAS253: THEORY OF STRUCTURES

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74/98

EAS253: THEORY OF STRUCTURES

About SFD and BMD on problems which are symmetry

w

1

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

75/98

EAS253: THEORY OF STRUCTURES

About SFD and BMD on problems which are symmetry

w

12

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

76/98

EAS253: THEORY OF STRUCTURES

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

Q2 Q2 Q2

Q1Q1Q1

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

77/98

EAS253: THEORY OF STRUCTURES

EAS253: THEORY OF STRUCTURES

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78/98

EAS253: THEORY OF STRUCTURES

Solution

AY

EY

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

79/98

EAS253: THEORY OF STRUCTURES

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

80/98

EAS253: THEORY OF STRUCTURES

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

81/98

EAS253: THEORY OF STRUCTURES

other

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

82/98

EAS253: THEORY OF STRUCTURES

EAS253: THEORY OF STRUCTURES

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83/98

EAS253: THEORY OF STRUCTURES

- Member BC (=member DC)

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

84/98

EAS253: THEORY OF STRUCTURES

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

85/98

EAS253: THEORY OF STRUCTURES

EAS253: THEORY OF STRUCTURES

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86/98

EAS253: THEORY OF STRUCTURES

3

45

EAS253: THEORY OF STRUCTURES

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87/98

x

x

5

4

x

5

3

EAS253: THEORY OF STRUCTURES

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88/98

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

89/98

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

90/98

Complete SFD obtained by

consideration of symmetry

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

91/98

Complete SFD obtained by

consideration of symmetry

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

92/98

Complete BMD obtained by

consideration of symmetry

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

93/98

BC:

AB:

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

94/98

sign of curvature(=sign of

bending moment changes)

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

95/98

BMD drawn using two different ways : drawn on compression side

and drawn on tension side

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

96/98

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

drawn on tension side

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

97/98

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

drawn on tension side

EAS253: THEORY OF STRUCTURES

7/26/2019 SFD and BMD in Frames

98/98