tn-328 design mxy floor pro 1

8/8/2019 TN-328 Design Mxy Floor Pro 1

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Technical Note Your Partner in Structural Concrete Design

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TN328_Design_Mxy_Floor_Pro_1030209

DESIGN FOR TWISTING MOMNETS IN ADAPT FLOOR-PRO

Update: March 2, 2009

This Technical Note explains (i) ADAPT-Floor Pros option for reporting the design values on a designsection in terms of twisting moment Mxy, normal shear, and inplane shear, and (ii) a conservativedesign procedure for the twisting moments. The conservative procedure is based on the Wood-Armerapproach, as implemented in the Canadian Code [CSA-A23.3-04, 2004].

Figure 1 illustrates an arbitrary design section of finite width and three of the six actions that in generalare present on a design section. The three components shown in the figure contribute to the torsion ofthe section. The two shear components are generally handled in shear design of the section. The focus

of this Technical Note is to present the procedure for design of the remaining component, namely thetwisting moment Mxy.

Twisting moment Mxy: This is a free vector acting on the section. It is shown to act on thecentroid of the section for convenience.

Normal Shear: This is the force that oftentimes is referred to as vertical shear and acts in theplane of the design section.

Inplane Shear: This force acts parallel to the reference plane of the design section (referenceplane is a user defined horizontal plane, mostly the uppermost top surface of a floor system).

FIGURE 1 VIEW OF A DESIGN SECTION


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Technical Note

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The Wood-Armer approach combines the design of the twisting moment Mxy with that of the bendingmoments Mxx and Myy. The following quote from the Canadian building code [CSA Standard, 2004]explains the details.

Section 13.6.4When reinforcement is placed as an orthogonal mat in the x and y directions, the factored

design moments shall be adjusted to account for the effects of torsion. In lieu of moredetailed calculations, the design moment intensities, mx,des

1or my,des, in the x and y

directions at any point shall be computed as follows:

(a) Positive design moments

mx,des= mx + |mxy|my,des= my + |mxy|

If either of mx,desor my,des is negative, it shall be taken as zero

(b) Negative design moments

mx,des

= mx - |mxy|my,des= my - |mxy|

If either of mx,desor my,des is positive, it shall be taken as zero

The above procedure is conservative. It is explained in greater detail in reference [McGregor, 1992].Note that in the context of the above prescription, positive moment is associated with tension andreinforcement at bottom, and negative moment with tension and reinforcement at top.

Numerical Example 1

At a given design section, the calculated design values are:

Mx = 500 kNmMxy = -200 kNm

Since the sign of the moment is positive, it relates to bottom reinforcement. Hence

For bottom rebar

Mx,des = 500 + |-200| = 500 + 200 = 700 kNm

For top rebar

Mx,des = 500 - |-200| = 500 - 200 = 500 kNm, (assume zero, since value is positive)

Numerical Example 2

At a given design section, the calculated design values are:

Mx = - 150 kNm

1mx,des and similar terms of the Canadian code are the moments for strength code check in Floor Pro


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Mxy = - 260 kNm

Since Mx is negative, it is associated with the reinforcement at top (negative design moment)

For positive (bottom) rebar

Mx = -150 + |-260| = -150 + 260 = + 110 kNm

For negative (top) rebar

Mx = -150 - |-260| = -150 -260 = -410 kNm

Observe that in this instance, reinforcement will be required for the both top and bottom of aslab. If a slab is post-tensioned, it is possible that tendons provide adequate capacity for bothpositive and negative moments, in which case no reinforcement will be required.

REFERENCES

Canadian CSA Standard, 2004, Design of Concrete Structures, A23.3-4, Canadian StandardsAssociation, Ontario, Canada, pp. 213, 2004

MacGregor, J., (1992), Reinforced Concrete Mechanics and Design, Prentice Hall, NJ, pp. 848, 1992

tn-328 design mxy floor pro 1

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