Torsion: Reinforced Concrete Members

[UmarMakhzumi]

*SEFP Consistent Design*

*Torsion: Reinforced Concrete Members *

*Doc No: 10-00-CD-0001*

*Date: May 24, 2013*

 

Torsional forces, generally speaking, occur in combination with flexural and transverse shear forces. From a design perspective, we need to understand difference between two torsion types:             

1. Compatibility Torsion
2. Equilibrium Torsion

Compatibility Torsion

Compatibility Torsion is when a member twists to maintain deformation compatibility; its induced in structural members by rotations (twists) applied at one or more points along the length of member. The twisting moments induced are directly dependent on the torsional stiffness of the member. These moments are generally statically indeterminate and their analysis necessarily involves (rotational) compatibility conditions(click on the image to enlarge).

 

 

For the floor beam system shown above, the flexure of the secondary beam BD results in a rotation ǾB at the end B. As the primary (spandrel) beam ABC is monolithically connected with the secondary beam BD at the joint B, deformation compatibility at B implies an angle of twist, equal to ǾB at spandrel beam ABC, and a bending moment will develop at the end B of beam BD. The bending moment will be equal to, and will act in a direction opposite to the twisting moment, in order to satisfy static equilibrium. The magnitude of ǾB and the twisting/ bending moment at B depends on the torsional stiffness of the beam ABC and the flexural stiffness of beam BD.

 

Now here is the fun part, the torsional stiffness of a reinforced concrete member is significantly reduced by torsional cracking. So, if you don’t design your spandrels for compatibility torsion, they will crack, increasing Ǿ_B and reducing the induced twisting moment. To paint the same picture while using ETABS, set your torsional stiffness of the main beam to zero. This will also increase the amount of flexural reinforcement in your secondary beams.

 

Moreover, considering design practice in Pakistan (since we never design beams without shear reinforcement), compatibility torsion can be ignored for regular structures, as minimum shear reinforcement in most cases would stand up to cracking torque. From ACI 318 commentary R11.6.1,

Torques that do not exceed approximately one-quarter of the cracking torque Tcr will not cause a structurally significant reduction in either the flexural or shear strength and can be ignored.

 

Do note that there are some situations (such as circular beams supported on multiple columns) where both equilibrium torsion and compatibility torsion coexist. Also, eccentrically loaded beams, member curved in plan, and member of space frames will be subjected to torsion. See the attached “Timesaving-TorsionDesign-IA.pdf” as a go-by. Timesaving-TorsionDesign-IA.pdf

 

 

Equilibrium Torsion

In simplest words, Torsion is a limit state in this condition; a structure is subjected to equilibrium torsion when it can maintain equilibrium only by resisting the torsion.  In such a case, torsional moment cannot be reduced by redistribution of internal forces since the torsional moment is required for the structure to be in equilibrium. From ACI- 318 (click on the image to enlarge).

 

 

 

 

Moreover, see the structures below that defy gravity when subjected to different kind of loads by standing up to equilibrium torsion.

 

Overall Building Torsion

For overall building torsion, the torsional effects can be minimized by reducing the distance between the center of mass and center of rigidity. Center of Mass is the point where the mass of an entire story is assumed to be concentrated. The center of mass is crucial as the location of seismic force at a particular level depends upon it.  The distance between the Center of Mass and the Center of Rigidity should be minimized, but may not be possible due to building geometry. Invariably, effects of torsion are present in at all buildings although analysis may show that in some buildings torsional effects are negligible. 

[EngrUzair]

Thanks for a good informative article on torsional aspects of RC members.  However, it is suggested that references to relevant codes or documents should be complete, for easy following of information and checking back the original reference for further study. For example, it took me a while to figure out which edition was being referred to, since the year of ACI 318 being referred was missing.

 

Accordingly, a little addition of references.

 

The above article refers generally to section 11.6 of 2005 edition of ACI 318 (ACI 318-05). In 2008 and 2011 editions (ACI 318-08 and ACI318-11), however the relevant information has been moved to section 11.5. The quote portion, in new codes, is in section R11.5.1, and the new figure numbers are Fig. R11.5.2.1 and R11.5.2.2 respectively.

[UmarMakhzumi]

Thanks Uzair

[Saiful Islam Zaber]

When does this appear in Etabs  "OS#45 "Shear Stress due to Shear Force and Torsion Exceeds Maximum Allowed".

[EngrUzair]

This warning message appears in cases, where the calculated value of shear and torsion stresses, EXCEEDS the value permitted by the code.

 

Generally, it requires increase in the member cross-section.

 

Regards.

[Saiful Islam Zaber]

You mean T_u  <= ǾT_{n ????}

[EngrUzair]

Assalam-o-alaikum!

 

Refer to ACI 318-08 Sections 11.5.3.1 and R11.5.3.1 for proper description & explanation.

 

 

Regards.

[UmarMakhzumi]

I was browsing through code and noticed something I thought would share as this question keeps coming in the forum. It is about when to consider torsional stiffness and when to ignore it.

Thanks.

Quote

R8.7 — Stiffness 

Two conditions determine whether it is necessary to consider torsional stiffness in the analysis of a given structure: (1) the relative magnitude of the torsional and flexural stiffnesses, and (2) whether torsion is required for equilibrium of the structure (equilibrium torsion) or is due to members twisting to maintain deformation compatibility (compatibility torsion). In the case of compatibility torsion, the torsional stiffness may be neglected. For cases involving equilibrium torsion, torsional stiffness should be considered. 

 

[Waqas Haider]

If i reduce my torsion constant to 0.01, having in mind that it is only needed for compatibility, The moment will transfer to slab and secondary beams and ultimately equilibrium will be obtained. But I m confused to achieve this equilibrium, the main beam need to twist for compatibility until equilibrium is achieved. This will induce diagonal cracks in main beam. Is it acceptable and with in serviceable limits? Are these hairline cracks dont affecting any thing especially appearance or any other design force?

I have also seen an approach of providing moment release to secondary beams to avoid excessive torsion and to get same condition physically reinforcement at joints of secondary  beams is provided to resemble pin support. But still i m confuse if this type of reinforcement is provided, the secondary beam section will crack. Are these cracks in acceptable limit?

[Ayesha]

7 hours ago, Waqas Haider said:

The moment will transfer to slab and secondary beams and ultimately equilibrium will be obtained. But I m confused to achieve this equilibrium, the main beam need to twist for compatibility until equilibrium is achieved.

 

7 hours ago, Waqas Haider said:

Are these cracks in acceptable limit?

You can let the main beam crack. You know the applied force and you can calculate the stress due to force and subsequent crack width.

 

[Waqas Haider]

Here I am confused regarding two things... 1st is how much we can reduce our design torsion Tu? If we reduce modifier to 0 or 0.01 it means we are reducing Tu completely...

But according to ACI  11.5.2.2 —

In a statically indeterminate structure where reduction of the torsional moment in a member can occur due to redistribution of internal forces upon cracking, the maximum Tu shall be permitted to be reduced to the values given in (a), (b), or (c), as applicable:
(a) For nonprestressed members, at the sections
described in 11.5.2.4 

φ4λ fc ′. Sqrt(Acp^2/pcp)

ans Section 11.5.2.4 says 

"11.5.2.4 — In nonprestressed members, sections located less than a distance d from the face of a support shall be designed for not less than Tu computed at a distance d. If a concentrated torque occurs within this distance, the critical section for design shall be at the face of the support."

 

It is saying in first clause that we can reduced our torsion upto minimum of φ4λ fc ′. Sqrt(Acp^2/pcp). So reducing modifier upto negligible value is confusing me. More over how to cater this reduction upto specified limiit of φ4λ fc ′. Sqrt(Acp^2/pcp)?

In 2nd paragraph it is relating torison design for distance less than d to the distance equal or greater than d. Is it a generalized statement or it is specifically saying that this minimum Tu requirement is for the distances less than d and for distances greater than d these can be ignored? 

Thanks.  

[UmarMakhzumi]

Hi Waqas,

Please see the following post:

The use of null modifiers for compatibility torsion like 0.001 arises out of convenience only. It is justified for situations such as compatibility torsion as we as design engineers can force alternate load paths at our discretion (nothing wrong with that).

Thanks.

[Waqas Haider]

This is from Book "Reinforced Concrete Design of Tall Buildings by Bungale S. Taranath"

From an inspection of the given problem, determine if the design torsion, Tu, is due to equilibrium torsion or due to compatibility torsion. If it is due to equilibrium, design of member for the entire calculated torsion. If Tu is due to compatibility requirements, as in statically indeterminate structures, it is permissible to reduce Tu to a maximum value, To given by
φ4λ fc ′. Sqrt(Acp^2/pcp)

Why ACI is putting limit on reduction if we can reduce upto negligible values?

 

Moreover,kindly explain the following wording by the same book.

 

Overall Building Torsion

Regarding the simultaneous application of loads in two mutually perpendicular directions, it is worth noting that for buildings in SDC B, the earthquake loads are assumed to act independently along the two orthogonal axes of the buildings. For SDC C buildings having nonparallel lateral load–resisting systems, and for all buildings in SDC D and higher, 100% of the forces for one direction are added to 30% of the forces in the perpendicular direction, the directions chosen to give the worst effect for the member being designed.

Is it necessary for every type of building in SDC D and higher? I though this clause is for only non parallel lateral load resisting systems. 
 

 

 

[UmarMakhzumi]

1 hour ago, Waqas Haider said:

This is from Book "Reinforced Concrete Design of Tall Buildings by Bungale S. Taranath"

From an inspection of the given problem, determine if the design torsion, Tu, is due to equilibrium torsion or due to compatibility torsion. If it is due to equilibrium, design of member for the entire calculated torsion. If Tu is due to compatibility requirements, as in statically indeterminate structures, it is permissible to reduce Tu to a maximum value, To given by
φ4λ fc ′. Sqrt(Acp^2/pcp)

Why ACI is putting limit on reduction if we can reduce upto negligible values?

 

 

 

ACI provides minimum design recommendations. You can go ahead and comply with them. As Engineer of Record, you are bound to stick with Building Code (ACI is not a building Code) and you can also exercise your engineering judgement in cases where you deem it necessary. Like I said, nothing wrong with it. If you want to reduce compatibility based on above quoted equation, please do so, but others that don't want to follow that approach can also do that.

 

1 hour ago, Waqas Haider said:

Overall Building Torsion

Regarding the simultaneous application of loads in two mutually perpendicular directions, it is worth noting that for buildings in SDC B, the earthquake loads are assumed to act independently along the two orthogonal axes of the buildings. For SDC C buildings having nonparallel lateral load–resisting systems, and for all buildings in SDC D and higher, 100% of the forces for one direction are added to 30% of the forces in the perpendicular direction, the directions chosen to give the worst effect for the member being designed.

Is it necessary for every type of building in SDC D and higher? I though this clause is for only non parallel lateral load resisting systems. 

I don't know the context, but based on what has been posted, the author for the book recommends all building in SDC D to be checked for 100% one direction + 30% perpendicular direction. As far as design practice goes, I haven't designed anything classified as a building in last 7 years so don't know what the current codes state about the requirement.

Thanks.

 

 

[Waqas Haider]

Kindly clarify my confusion in either thread. Thanks. 

 

[UmarMakhzumi]

Hi Waqas,

I have seen your updated post. What you have quoted in correct and as per ACI recommendations. What I am trying to highlight is that we don't need to worry about compatibility torsion for typical beam-column, two way slab concrete frame structures because - and I will quote my above reply here:

On 2017-03-23 at 11:38 AM, UmarMakhzumi said:

As Engineer of Record, you are bound to stick with Building Code (ACI is not a building Code) and you can also exercise your engineering judgement in cases where you deem it necessary. Like I said, nothing wrong with it. If you want to reduce compatibility based on above quoted equation, please do so, but others that don't want to follow that approach can also do that.

The approach of 0.001 is used because ACI minimum design recommendations are too conservative for compatibility torsion for beam-column two way slab structure (what we have in Pakistan 99% of the time). That is why you never see any serviceability failures due to compatibility torsion (the other reason could be the tendency to over-reinforce structure but lets focus on this one for now).

You can follow the guideline but those who don't follow it (like myself), do it for the reason explained above. The difference here is the same as difference between laws and traditions. Laws are there but people tend to incline towards tradition. So, probably we can blame our innate tribalism for following such stuff and not code.