1

Design for Torsion by ACI 318-11

Basile G. Rabbat

Consultant Mt. Prospect, IL

bgrabbat@gmail.com

September 25- 26, 2013

Learning Objective

Determine when design for torsion is mandated by Code

Distinguish between: Equilibrium Torsion Compatibility Torsion

Design torsion reinforcement Detail torsion reinforcement

2!

3!

Two-Way Flat Plate w/Spandrel Beams (13.6.3)

3!

Design spandrel for torsion

2

4!

Torsion in Canopy Spandrel Beam

Design for Torsion

11.5 Design for Torsion

Based on Thin-Wall Tube, Space Truss Analogy

Applies to: R/C & P/S Hollow and Solid Sections

Tc = 0 5!

Solid vs. Hollow Section Strength

6!Source: MacGregor, ACI 318-11 Ref. 11.31

3

R11.5 Thin-Wall Tube Analogy

7!

!

8!

11.5 Design for Torsion

Compute Tu (from analysis) If Tu < Tcr /4 (threshold torsion)

Ignore torsion Cracking at = 4 fc If Tu Tcr /4 Design for torsion

Equilibrium torsion? Compatibility torsion?

Design torsion reinforcement Transverse & longitudinal reinf.

!

11.5.1(a) Threshold Torsion

Nonprestressed Concrete

Threshold torsion (Tcr /4)

Tu < !" fc' Acp

2

pcp

!

"##

$

%&&

9!

4

11.5.1(b) Threshold Torsion

Prestressed Concrete

Tu < !" fc' Acp

2

pcp

!

"##

$

%&& 1+

fpc4" fc

'

fpc = compressive stress in concrete, after prestress losses, at centroid of cross section

10!

11.5.1(c) Threshold Torsion

Nonprestressed w/Axial Force

Tu < !" fc' Acp

2

pcp

!

"##

$

%&& 1+

Nu4Ag! fc

'

Nu = factored axial force normal to cross section occurring simultaneously with Vu or Tu; positive for compression and negative for tension

11!

12!

11.5.1 Acp & pcp

Members cast monolithically with a slab Effective flange width per 13.2.4

h (h hf ) 4hf

hf

bw

Acp = Shaded area pcp = Perimeter of shaded area

5

11.5.1 Threshold Torsion

Determine Acp and pcp

Neglect overhanging flange(s) when:

Acp2 pcp

Beam w/o flange(s)

Acp2 pcp

Beam with flange(s) <

13!

11.5.1 Threshold Torsion

Hollow sections

Replace Acp with Ag in equations for threshold torsion

14!

15!

R11.5.2.1 Equilibrium Torsion

Design torque may not be reduced, because moment redistribution is not possible

6

16!

R11.5.2.2 Compatibility Torsion

Design torque for spandrel beam may be reduced because moment redistribution is possible

17!

11.5.2.2 Compatibility Torsion

Twist

Tcr Torque

Tn

Tu,comp = 4 fc Acp2 pcp

= Tu,comp

18!

11.5 Design for Torsion - Recap

Compute Tu (from structural analysis)

If Tu < Tcr /4 Ignore torsion

Tu Tcr /4 Design for torsion Equilibrium torsion? Design for Tu (analysis) Compatibility Torsion?

Design for Tu,comp = Tcr (compatibility) Redistribute T = Tu Tu,comp = Tu - Tcr

7

11.5.2.2 Compatibility Torsion, Tu,comp

19!

Tu ! !4" fc' Acp

2

pcp

"

#$

%

&' 1+

fpc4" fc

'

Tu ! !4" fc' Acp

2

pcp

"

#$

%

&' 1+

Nu4Ag" fc

'

Tu ! !4" fc' Acp

2

pcp

"

#$

%

&'

R/C w/Axial Force

P/S

R/C

Note: Do not replace Acp with Ag

11.5.2.3 Slab/Spandrel Torsion

Determine torsional moment distribution through analysis

Assume torsion from slab to spandrel to be uniformly distributed

20!

11.5.2.4-.5 Critical Section

Distance from support R/C d

P/S h/2

Exception: Concentrated torque within distance d (R/C), or h/2 (P/S)

21!

8

Torsional Stresses Shear Stresses

11.5.3.1 Adequacy of Solid Section

22!

11.5.3.1 Adequacy of Solid Section

Circular interaction

23!

Vubwd

!

"#$

%&

2

+Tuph1.7Aoh

2

!

"#$

%&

2

' !Vcbwd

+8 fc'!

"#$

%&

Torsional Stresses Shear Stresses

11.5.3.1 Adequacy of Hollow Section

24!

9

11.5.3.1 Adequacy of Hollow Section

Linear interaction

25!

Vubwd

!

"#$

%&+

Tuph1.7Aoh

2

!

"#$

%&' !

Vcbwd

+8 fc'!

"#$

%&

11.5.3.3 Thin Wall Section

If t < (Aoh /ph ) Replace

26!

Tuph1.7Aoh

2

!

"##

$

%&& with

Tu1.7Aoht

!

"##

$

%&&

Space Truss Analogy Torsional Cracks Spiral Around Section

27!Courtesy : Dr. Michael Collins, University of Toronto

10

28!

Concrete Shell Spalls

Courtesy : Dr. Michael Collins, University of Toronto 28!

Stress Trajectories Tension in Hoop

Compression in Concrete

Compression in Concrete

Tension in Hoop

Outside of Concrete

Source: Collins & Mitchell, Prestressed Concrete Structures

Concrete Shell Spalls

29!

11.5.3 At Maximum Torque

Concrete shell spalls

Aoh = Area within stirrup centerline

Assume Ao = 0.85Aoh

30!

11

Fig. R11.5.3.6(b) Definition of Aoh

31!

32!

T

Longitudinal Bar

xo

yo

Stirrups Cracks

= 30o to 60o

V1 V2

V3

V4

R11.5.3.6(a) Space Truss Analogy

Concrete Compression Diagonals

For R/C = 45o For P/S = = 37.5o

33!

11.5.3.6 Transverse Reinforcement

Atfyt

yocot

s

yo = center-to-center length of closed stirrup

V2

Atfyt

V2 =qyo =T2Ao

yo =Atfytsyo cot!

12

34!

11.5.3.6 Transverse Reinforcement

Atfyt

yocot

s

yo = center-to-center length of closed stirrup

V2

Atfyt

Tn =2AoAtfyts

cot!

where Ao = 0.85Aoh = 0.85xoyo

11.5.3.6 Torsional Moment Strength

Tn Tu

35!

= 0.75 (9.3.2.3)

Tn = 2Ao At fyt

s cot (11-21)

11.5.3.6 Transverse Reinforcement

Determine transverse reinforcement required for torsion

36!

=

Ao = 0.85Aoh

At s

Tu (or Tu,comp) 2Aofyt cot

13

11.5.5.2 Minimum Transverse Reinf.

37!

Av At s

+ Minimum = 0.375 f c bws

fyt

25bw fyt 2s

Av = 2fyt d

2s Vu Vc

38!

11.5.3.7 Longitudinal Reinforcement

N2 /2

N2 /2

N2

D2 V2

yo cos

yo

N2 =V2 cot! =A!fy

V2 =Atfytsyo cot!

Afy/2

39!

11.5.3.7. Longitudinal Reinforcement

N2 /2

N2 /2

N2

D2 V2

yo cos

yo

A! =Atsphfytfycot2!

ph = perimeter of centerline of exterior stirrup/hoop

Afy/2

14

40!

11.5.3.7 Longitudinal Torsional Reinf.

A =

s

ph

fyt

fy

cot2 (11-22) At

41!

11.5.5.3 Minimum Longitudinal Reinf.

A,min =

5 fc Acp

fy ph

s

At

fyt

fy

At s

25bw fyt

11.5.3.6-.7 Torsion Reinforcement

42!

h

bw

At @ s

A"

15

Determine longitudinal reinforcement required for flexure

Combine longitudinal reinforcement required for torsion with that required for flexure A added to Aflexure on tension side A may be reduced in flexural compression

zone of member by Mu/(0.9dfy) 43!

11.5.3.9 Details of Longitudinal Reinforcement

11.5.6.2 Details of Longitudinal Torsional Reinforcement

44!

Minimum one longitudinal bar in every corner

12 (typ.)

11.5.6.2 Details of Longitudinal Torsional Reinforcement

45!

16

db s/24

db 3/8

46!

11.5.6.2 Details of Longitudinal Torsional Reinforcement

Extend torsion reinforcement beyond theoretical cut-off point a distance of (bt + d)

47!

11.5.6.3 Details of Torsion Reinforcement

11.5.6 Spacing of Transverse Reinf.

ph /8

12 in.

d/2

48!

17

Questions?

49!