Calculation of Strand Elongation

Calculation Of Elongation

The stressing records are part of the st ructural design and serve as a basis for the stressing operation. Besides the prestressing data, they contain sequence of stressing and directions for procedures directly connected with stressing operation, such as lowering of the formwork and releasing of bearings. calculation of strand tendon elongation at stressing

The total elongation

Itot

I p

Ip

=

It ot

which the tendon has to achieve during stressing should be calculated as:

Ic

+

+

Isl

+

Ie

= elongation of the strand tendon [mm] lp

Ip =

1 Ap · Ep

·

lp

∫ 

lc

= length of tendon [m]

Px,0·dx

0

2

Po

Px,0 = prestressing force of the tendon at any point distance x [kN]  P = P · e-µ· X

1

                      

x,0

P0

= prestressing force at the stressing end [kN]

x

= ∑ angle of deflection between the stressing end and at any point distance x [rad]

                      

=

                       

3

0



[ aH + aV + ß·|] 2

180

Po Pe

2

µ

= coef coeffi fici cien entt of fri fricti ction on (se see e p.5 p.5))

ß

= wob wobbl ble e ang ngle le (se see e p. p.5) 5)

Pe

= prestressing force at the stressing end after unintentional slip

le

of elongation [kN]

I c

= elastic deformation of the concrete (shortening must be treated as a positive value) [mm]

Ic

=

cm

Ec



· lc

cm

lc

I sl

lsl [mm]

= sum of anchor plates impressions and dead end wedge slip according anchorage type applied [mm]

accessible inaccessible

= average stress in the concrete cross section at the centre of gravity of all tendons due to prestressing prestressing force [MN/m 2] = length of the concrete member [m]

life end anc horage 1 -

d ead end anc horage 4 3

Bond Head anc horage *)

Coup ler R 3

Coup ler D 6

Coupler M 3 -

*) see german approval I e

= elongation of the prestressing steel in the jack and seating device (if applicable) [mm]

Calculation of life end prestressing force Pe [kN] and influence length le [m]

due to life end wedge slip

Ie =

In

[mm] at release release of stressing stressing jack



                      

1

In

· Ep · Ap P0 · µ · 1

unintentional slip                       

= avera average ge angle of deflection along the influence length length l e of tendon behind the life end [rad/m]

                      

In

[mm]

t endon t yp e

jack t yp e st and ard c ase 4** 2* 8

Pe = P0 · (1 - 2 · l e· µ · 1) at the life end anchorage at the coupler M

6801 - 6807 6809 - 6827 6802 - 6812 *) with wedge seating

modulus of elasticity elasticity [N/mm 2]

**) without wedge seating

c oncret e class Ec

B 25 30,000 strand

required cube strength of the concrete at stressing acc. DIN 4227, part 1

sp ec ial case 2** 4 -

part ical prest ressing full prest ressing

B 35 34,000

B 45 37,000

B 55 39,000

Ep = 195,000 [N/mm2] 12 24

16 32

20 40

24 48