Post-tension Prestress Design

Post-Tensioning Prestress Analysis and Design Jane Li, PhD, PE April 2011

Outline • • • • •

Advantages and Diverse Applications Equivalent Load of Post-Tensioning Modeling in SAP2000 Design Examples

Advantages: Post-Tensioning • Longer span capacity with lower girder depth • Elegance • Green and economic solution, reduce super structure weight, reduce demand on substructure • Diverse applications, not only for new design, but also rehabilitation or retrofit, construction support, and so on…

Equivalent Load of Post-Tensioning e

T

T

P_axial=T M=P·e

Equivalent Load: Harp Strand e P_axial= Tcos( ); T

T;

Tcos( )

Fx Fy

T M=P·e(x)=

Fx=T-T·cos( )

Fy=T·sin( )

Fy·x;

T;

Fy·(L-x)

T·cos( ) Fy Fx Fy

Fx Fy

Note: if

is small, Fx 0

Equivalent Load: Arc Strand R P_axial T T

T

/2

/2

Fy=2T·sin( /2) 2T· /2= T· w=Fy/L= T· /(R· )=T/R ….LRFD 5.10.4.3.1-1

M=P·e=w·L2/8

T

T

T· /2

T· /2 wy T/R

Note: prestress loss ignored

Equivalent Load: Parabolic 1

3

2

(x1,y1)

(x3,y3)

(x2,y2)

T1

T2 2=y’2

1=y’1

Fy=T1· 1+ T2· 2;

wy=Fy/L

Fx=T2-T1;

wx=Fx/L

T2

T1 wy T1· 1 wx

Three points define a unique parabolic: y=ax2+bx+c

T2· 2

Tendon Element in SAP2000

Right click tendon

Tendon Element in SAP2000

Tendon Element in SAP2000