89

1.2.10 The model shall apply directly to both reinforced and

prestressed concrete members. The area of prestressed reinforcement

shall be transformed into an equivalent area of nonprestressed

reinforcement based on computed yield force capacity.

1.2.11 Adequate detailing of the reinforcement shall be

provided to prevent premature failures prior to yielding of this

reinforcement.

1.3 General Principles and Requirements

1.3.1 Design of members subjected to shear, or torsion, or to

combined shear and torsion, shall be based on a truss model with

variable angle of inclination of the diagonals resulting from use of the

assumptions in Section 1.2. For members with low levels of shear and

torsion stresses an additional concrete contribution to the nominal

strength may be included as specified in Sec.1.3.6.

1.3.2 The ratio of longitudinal reinforcement p provided

shall not exceed 0.75 of the ratio ~ that would produce balanced strain

conditions for the section under pure flexure without axial load.

1.3.3 The compression stress in the diagonal members of the

truss model shall not exceed the value:

30~ (1-6 )

1.3.4 For members subjected to torsion the truss analogy

shall be based on a space truss with variable angle of inclination of

the diagonals. The torsional resistance of the space truss may be

computed as the resistance of an equivalent thin walled tube. An

90

appl ied torsional moment may be considered to produce a constant shear

flow around the cross section.

q = T/2Ao ( 1-7>

1.3.4 For the case of solid cross sections subjected to

torsion an effective web thickness be shall be used. The effective web

thickness be shall be taken as the smaller of the two values

1.3.5 In members with ducts in the webs having a diameter dd

greater than 1/10 of the web, the effective web width shall be taken as

(1-9 )

for ungrouted ducts, and

bw - 0.67 U:ld (1-10)

for the case of grouted ducts. In determining Ldd' only the ducts in a

single critical plane should be considered.

1.3.6 An additional concrete contribution to the shear and

torsional strength of the member may be recognized in the design of the

transverse reinforcement as follows:

(a) For the case of shear in reinforced concrete members

Vc = (1/2)[6 ~ - vuJ bwz

but 0 ~ Vc ~ 2 Jfb bwz

(b) For the case of shear in prestressed concrete members

Vc = (K/2)[(4 + 2K) ~ - vuJbwz

but 0 ~ V c ~ 2K Jf' c bwz.

(1-11)

(1-12)

91

(c) For the case of torsion in reinforced concrete members

Tc = (1 /2 )[ 6 J'f':c' - v ] 2A b u 0 e (1-13)

(d) For the case of torsion in prestressed concrete members

Tc = (K/2)[(4 + 2K)Jfrc' - v 12A b (1-14) u 0 e

but 0 ~ Tc ~ 2K./f';. [2Aobe l

(e) K shall be computed as [1 + fps/2JiIJ O•5 but 1.0,S. K ,S. 2.0.

Furthermore, K shall be taken equal to 1.0 at all sections of the member

where the stress in the extreme tension fiber due to the computed

ultimate load and the applied effective prestress force exceeds the

val ue of 6J'J:

(f) For the case of combined shear and torsion, the concrete

contribution shall be distributed in part to shear, and in part to

torsion, as a function of the levels of shearing (vu(V» stress and

torsional (vu(T» stress in accordance with the following:

The value of Vc given by Sec. 1.3.6(a) or (b) shall be

mul tipl ied by

(1-15)

in the presence of combined shear and torsion.

The value of Tc given by Sec. 1.3.6(c) or (d) shall be

mul tiplied by

(1-16)

in the presence of combined shear and torsion.

1.3.7 In the design of the longitudinal steel required for

shear and/or torsion, the concrete contribution shall be taken as zero

92

when the factored shearing stress due to shear and/or torsion exceeds

the values of

2.ffic (1-11)

in reinforced concrete, and

K(2.J'16) (1-18)

in prestressed concrete members. The val ue of K shall be lim i ted as

specified in Sec. 1.3.6(e).

1.4 Detailing of the Reinforcement

1.4.1 Torsion

1.4.1.1 Members in which the torsional shearing stress

exceeds the value of ¢1.0../"fJ shall have a minimum amount of web

reinforcement equal to

(1-19)

1.4.1.2 Where the factored torsional moment Tu exceeds the

torsional moment strengtb ¢fc ' torsional reinforcement shall be provided

to satisfy Eqs. (1-3) and (1-4).

1.4.1.3 Longitudinal reinforcement required for torsion shall

be distributed around the perimeter formed by the closed stirrups. At

least one longitudinal bar shall be placed in each corner of the

stirrups. The minimum diameter of the corner bar shall be taken as 1/16

of the stirrup spacing but no less than that of a 03 bar.

1.4.1.4 Longitudinal reinforcement required for torsion shall

be adequately anchored to develop its full yield strength everywhere

within the section subjected to the torsional moment.