25

of the values suggested in both the ACI Building Code (2) and AASHTO

Stand ard Spec ific ations (1) of 2 ~ but no more than 3.5..f1"c.

In the case of prestressed concrete members an increased value

of the concrete contribution in the transition state is allowed, if for

the calculated ultimate load and for a given applied prestressing force

the resul ting extreme fiber stress does not exceed the value of 2vcu

(e.g. at the support regions of a pretensioned beam). Note that this is

similar to a tensile stress of 6 to 6.6~. This limit in effect

introduces a Vci check into the Swiss procedure. The allowed concrete

contribution in the case of prestressed concrete members is shown in

Fig. 2.7.

In order to avoid failures due to crushing of the web, the

nominal shear stress vn evaluated using the nominal shear force Vn = Vs

+ Vc must not exceed the values vmax ' which are dependent upon the

concrete strength and the maximum stirrup spacing.

- vmax = 5vcu for smax = z/2 but s < 12 in.

vmax = 6vcu for smax = z/3 but s < 8 in.

A comparison between these two limits and the upper limit

suggested in the ACI Code (24) and AASHTO Standard Specs. (1) of 10J'fj

is shown in Fig 2.8. The Swiss Code allows much higher shear stresses.

The design procedure for the case of torsion in the Swiss Code

follows the same lines as the truss model. The Swiss Code design

procedures are applicable to both reinforced and partially prestressed

or fully prestressed concrete members, provided their warping resistance

is neglected. As in the CEB-Refined method, torsional moments, as a

26

~Veu

Vc: concrete contribution

transition =~Mo+--

__ ..... ,~I_~FU.;;..I;..;;.I ... tru88 action

ve=~ [(2+~ lVeu-V]:; 0

~ I

:~ I I

~ Veu

~=~+ Fse Ac·Vcu

(2+~lVeu

Vu shear stress

F Prestressing force under service load condition se

A Cross-sectional area of the concrete c

Fig. 2.7 Concrete contribution in the case of prestressed concrete members

27

V max (p s i )

2000

6 Vcu

1000 ~ 5Vcu

~----IO:-,lf-;:fC fc (psi)

(000) 2 :3 4

Fig. 2.8 Comparison between the upper limit for the shear stress in a section

5

rule, are only to be taken into account in the design if they are

necessary for equil ibrium. For compatibility torsion, the only

requirement is that some reinforcement be placed to control crack

development. No specific information is given as to how to evaluate

this required amount of reinforcement.

The limits for the angle of inclination of the diagonal strut

remain those presented in Eq. 2.1.

The torsional moment for the calculated ultimate load must be

equal or less than the resistance value. The resistance value is made

up of the resistance Ts carried by the truss, and the additional

resistance of the concrete Tc in the transi tion range between the

uncracked state and the full truss action.

28

The amount of torsion carried by the truss with vertical

stirrups is given by Eq. 2.19.

where Ao is the area described by the perimeter enclosing the

longitudinal reinforcement.

Due to the inclination of the compression field in the truss

model an additional area of longitudinal reinforcement is required to

resist the horizontal component of the inclined compression field which

is assumed to be acting at the centroid of the perimeter u around the

area Ao. The additional area is evaluated using Eq. 2.20.

(2.20)

where Al (T) is the total area of longitudinal steel required to resist

the tension force produced by the torsional moment Tu. Eq. 2.20 follows

directly from Eq. 3.30 derived in Sec. 3.4 of Report 248-2 from

equilibrium considerations in the truss model.

The concrete contribution in the transition state is the same as

the one assumed for the case of shear shown in Figs. 2.6 and 2.7 for

reinforced and prestressed concrete respecti vel y.

The shear stress due to torsion is evaluated using Eq. 2.21

(2.21)

which as in the CEB-Refined method, is derived from the theory of thin­

walled cross sections. The value "be" represents the effective wall