LOAD ONLY BEAM SUBJECT TO POST-TENSIONING

dearmeltedUrban and Civil

Nov 25, 2013 (3 years and 4 months ago)

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(b) BEAM DETACHED FROM SUPPORTS

(a) THREE SPAN POST
-
TENSIONED BEAM

LOAD ONLY

BEAM SUBJECT TO POST
-
TENSIONING

LINE OF SUPPORTS

A

B

DISPLACEMENT d

C

TENDON

FORCE P

TENDON

D

HYPERSTATIC (SECONDARY)

SUPPORT REACTIONS (HYPERSTATIC MOMENTS)

(b) MOMENTS DUE TO PRESTRESSING

(a) REACTIONS AT SUPPORTS DUE TO

PRESTRESSING (HYPERSTATIC REACTIONS)

REACTIONS AND MOMENTS

A

R

i

B

MOMENT

REACTION

C

D

THE CORRESPONDING INTERNAL DISTRIBUTION

SECTIONAL ACTIONS DUE TO PRESTRESSING &

AT STRENGTH LIMIT STATE

(b) ASSUMED INTERNAL FORCE DISTRIBUTION

R

R

(a) RESULTANT MOMENT AND SHEAR AT

A SECTION

OF FORCES AT STRENGTH LIMIT STATE

REACTION

A

REACTION DUE TO

POST
-
TENSIONING

A

CONCRETE

COMPRESSION

TENDON FORCE

T

i

C

z

HYP

B

i

X

i

V

M

HYP

B

POST
-
TENSIONED FRAME UNDER LOADING

TN7
-
351

LL = LIVE LOAD

DL = DEAD LOAD

TENDON

PT

DL

LL

POST
-
TENSIONING

SUPPORT REACTIONS DUE TO

M

JOINT 1

1

R

M

M

JOINT i

1

b

R

t

1

i

M

TN7
-
150

PT

b

i

i

t

ACTIONS CAUSING HYPERSTATIC

MOMENTS AND SHEARS

TN7
-
143

M

X

i

X

1

1

R

M

M

R

b

1

1

t

M

i

b

i

i

t

PT

HYPERSTATIC MOMENT (M) AND

SHEAR (V) IN A SECTION

TN7
-
319

POST
-
TENSIONING

X

1

1

R

M

b

1

M

t

1

R

i

V

b

M

X

i

i

M

t

i

M

COLUMN

x 450mm

(a) PLAN

GEOMETRY OF THREE SPAN TWO
-
WAY SLAB

(b) ELEVATION

300mm

8.20m

(c) TENDON GEOMETRY

1237.5kN

25

EQ

EQ

WALL

200mm

130

EQ

235

5.75m

260mm

200mm

1600mm

130

x 1100mm

x 200mm

(Y
-
SCALE EXAGGERATED)

1650kN

EQ

25

EQ

235

EQ

25

163

TN7
-
503

0.90m

6.75m

DROP CAP

1600

mm

3.00m

2.50m

(UNITS kN
-
m)

(UNITS IN kN AND kN
-
m)

8.20m

SLAB DESIGN STRIP

HYPERSTATIC ACTIONS OF THE TWO
-
WAY

(b) DISTRIBUTION OF HYPERSTATIC MOMENTS

(a) HYPERSTATIC ACTIONS AT SUPPORTS

51.65

25.82

EQ

41.82

41.87

2

1

5.75m

8.983

-
8.972

9.834

41.91

225

SUPPORT

FACE OF

IN
-
SPAN

EQ

mm

4

3

6.75m

18.870

60.78

-
9.015

9.005

0.90m

TN7
-
505

DISTRIBUTION OF POST
-
TENSIONING MOMENT

SPAN 2

SPAN 1

300

200

100

-
100

0

-
200

CANT

SPAN 3

TN7
-
514

BELOW SLAB

600 X 600mm TYP. UNO.

DROP PANEL

0.3m

C

STRUCTURE PLAN

SLAB 250

9.6m

500mm

1

B

0.3m

A

OPENING

600 DIA.

4.0m

8.7m

6.7m

2

3

TN7
-
456

mm

TENDON LAYOUT

NOTE:

STRESSING END

TENDON CGS ABOVE SLAB SOFFIT

50mm AT LOW POINT

200mm AT HIGH POINT

125mm AT SLAB EDGE

C

A

B

12T

5T

4T

27T

1

BANDED

TENDONS

DISTRIBUTED TENDONS:

3 STRANDS EACH, UNO.

DEAD END

12T MEANS 12 STRANDS

TN7
-
457

2T

1T

12T

2

3

DISTRINUTED TENDONS

TENSIONING ONLY (kN)

SUPPORT REACTIONS DUE TO POST
-

OPENING

C

Fz =
-
0.576

Y

X

A

B

Fz = 1.05

COLUMN

Fz = 47.8

1

Mx = 0.495 kNm

My = 0

Fz = 21.6

Fz = 8.61

TN7
-
458

Fz = 38.8

Fz = 2.18

Fz =
-
140

Fz = 20.3

DROP CAP

2

3

HYPERSTATIC MOMENTS, My

C

CONTOURS AT 10kN INTERVALS

CONTOUR PLOT OF

Y

X

0

4.97 kN

0

0

B

A

10

64.1 kN

-
10

-
10

0

0

10

10

10

10

20

20

10

30

40

10

10

30

10

10

10

20

10

10

1

0

0

-
0.366 kN

0.926 kN

0

0

2

0

0

-
10

0

0

0

3

TN7
-
459

HYPERSTATIC IN
-
PLANE FORCES AT LINE 2

176kN

(b) IN
-
PLANE ACTIONS AT LINE 2

(a) DISTRIBUTION OF IN
-
PLANE COMPRESSION

AT LINE 2

173kN

349kN

125mm

TENSION

-
176kN

103kN/m

349kN

1

TN7
-
508

COMPRESSION

-
9.33kN/m

-
69kN/m

-
77kN/m

-
2.38kN/m

-
173kN

C

B

A

2

3

(d) APPLICATION OF POST
-
TENSIONING

(c) CLOSURE OF SPLICE

(a) COMPLETED STRUCTURE

(b) INSTALLATION OF PRECAST GIRDERS

TWO SPAN SEGMENTAL CONSTRUCTION

80mm

POST
-
TENSIONING

20 m

300mm

80mm

8.28m

300mm

TN7
-
509

PRE
-
TENSIONING

80mm

300mm

20 m

(a)
DISTRIBUTION OF PRESTRESSING

MOMENTS DUE TO POST
-
TENSIONING

344 kNm

262 kNm

MOMENT IN THE COMPLETED STRUCTURE

(b) DISTRIBUTION OF HYPERSTATIC

MOMENT IN THE COMPLETED STRUCTURE

(b) DISTRIBUTION MOMENT DUE TO SELF WEIGHT

(a) DISTRIBUTION OF MOMENT DUE TO SELF
-

WEIGHT SEGMENTAL CONSTRUCTION

ONE STAGE CONSTRUCTION

99.8 kNm

-
172 kNm

171 kNm

SEC

MOMENTS

PRIMARY AND SECONDARY

BALANCED MOMENT M AS SUM OF

SEC

M (wdx)x

M + M ;

b

M

P

b

P

+ M

.

e

V

P

dx

a

X

w

A

A

i

+ R X

b

+ V a

OR

A

.

i

.

M

i

X

R

b

V

B

P

b

DISTANCE a ALONG THE MEMBER

ILLUSTRATION OF PRIMARY MOMENT (M ) AT

M = (wdx)x + V a

(a) FREE BODY DIAGRAM OF CUT BEAM

(b) FREE BODY DIAGRAM OF CUT TENDON

P e= (wdx)x + V a

.

P

dx

A

.

V

A

w

V

P

P

A

dx

A

w

e
-
ECCENTRICITY

P

M = P e


; HENCE

a

P

X

V

x

.

P

PRIMARY MOMENT

a

A

.

X

V

x

O

COMPRESSION

P

M

P

B

W

W

(A)

AND POINT OF INFLEXION (B)

SECTION BETWEEN ITS LOW POINT

FREE BODY DIAGRAM OF A TENDON

B

A

W

P

P

V

AD61 (F3) 062089 BFL

REMOVAL OF TENDON

(a) FREE BODY DIAGRAM OF BEAM AFTER

P

V

W

V

P

V

W

V

P

P

TENDON

(b) FREE BODY DIAGRAM OF TENDON

ILLUSTRATION OF FORCE SYSTEM

A

B

C

D

A

D

A

D

BETWEEN TENDON AND BEAM

TENDON

THREE SPAN POST
-
TENSIONED BEAM

AD80 (F4) 062089 BFL

TENDON

THREE SPAN POST
-
TENSIONED BEAM

AD80 (F4) 062089 BFL

AD61 (F3) 062089 BFL

REMOVAL OF TENDON

(a) FREE BODY DIAGRAM OF BEAM AFTER

P

V

W

V

P

V

W

V

P

P

TENDON

(b) FREE BODY DIAGRAM OF TENDON

ILLUSTRATION OF FORCE SYSTEM

A

B

C

D

A

D

A

D

BETWEEN TENDON AND BEAM

(A)

AND POINT OF INFLEXION (B)

SECTION BETWEEN ITS LOW POINT

FREE BODY DIAGRAM OF A TENDON

B

A

W

P

P

V

DISTANCE a ALONG THE MEMBER

ILLUSTRATION OF PRIMARY MOMENT (M ) AT

(a) FREE BODY DIAGRAM OF CUT BEAM

(b) FREE BODY DIAGRAM OF CUT TENDON

P

dx

V

A

w

V

P

A

dx

A

w

e
-
ECCENTRICITY

P

a

X

V

x

P

PRIMARY MOMENT

a

X

V

x

O

COMPRESSION

P

M

P

B

W

W






a
V
x
wdx
M
A
P


e
P
M
hence
;
a
V
x
wdx
e
P
P
A







(b) BEAM DETACHED FROM SUPPORTS

(a) THREE SPAN POST
-
TENSIONED BEAM

LOAD ONLY

BEAM SUBJECT TO POST
-
TENSIONING

LINE OF SUPPORTS

A

B

DISPLACEMENT d

C

TENDON

FORCE P

TENDON

D

HYPERSTATIC (SECONDARY)

SUPPORT REACTIONS (HYPERSTATIC MOMENTS)

(b) MOMENTS DUE TO PRESTRESSING

(a) REACTIONS AT SUPPORTS DUE TO

PRESTRESSING (HYPERSTATIC REACTIONS)

REACTIONS AND MOMENTS

A

B

MOMENT

REACTION

C

D

THE CORRESPONDING INTERNAL DISTRIBUTION

SECTIONAL ACTIONS DUE TO PRESTRESSING &

AT STRENGTH LIMIT STATE

(b) ASSUMED INTERNAL FORCE DISTRIBUTION

R

R

(a) RESULTANT MOMENT AND SHEAR AT

A SECTION

OF FORCES AT STRENGTH LIMIT STATE

REACTION

A

REACTION DUE TO

POST
-
TENSIONING

A

CONCRETE

COMPRESSION

TENDON FORCE

T

i

C

z

SEC

B

i

X

i

V

M

SEC

B



i
i
sec
X
R
M
z
C
z
T
M
sec


Τ
Χ

MOMENTS

PRIMARY AND SECONDARY

BALANCED MOMENT M AS SUM OF

V

P

dx

a

X

w

A

A

b

OR

M

i

X

R

b

V

B

P

b





sec
sec
P
i
i
A
b
M
e
P
M
M
X
R
a
V
x
x
d
w
M










BALANCED LOADING AND CHANGES

IN MEMBER THICKNESS

(e) ACTIONS CAUSING FLEXURE OF MEMBERS

(BALANCED ACTIONS)

(d) ACTIONS CAUSING AXIAL COMPRESSION

(b) BALANCED LOADING

P

P

P

NA

TENDON

m

P

M

p

b

w

w

m

M =Pm

(c)

P

m

b

P

P

(a)

NA

TN7
-
341

CENTROIDAL AXIS