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Technical Note

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TN320_Mxy_and_shears_102108

TWISTING MOMENT AND SHEARS ON DESIGN SECTIONS

This Technical Note explains ADAPT-Floor Pros option of reporting the design values on a designsection in terms of twisting moment Mxy, normal shear, and inplane shear. The alternative option of theprogram is to combine the effects of these three actions into a single torsion at the centroid of thedesign section (see TN305 ).

Figure 1 explains the features of this option. The three components that are specifically addressed inthis Technical Note are:

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 acts perpendicular to the plane of the design section,oftentimes referred to as vertical shear. The plane of the design section is the reference planedefined by the user. The top and bottom surfaces of the geometry sections of a design sectionare parallel to the reference plane. But a design section can have steps, changes in thicknessand voids as indicated in the figure.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

8/8/2019 TN-320 Mxy and Shears

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Technical Note

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An example of the tabular report of the values explained above is shown below:

Load Combination:ULS3a

ecc = Eccentricity for forceNormal shear eccentricity (ecc) is the distance from the first end of design section toward the second endInplane shear eccentricity (ecc) is the distance from the centroid of design section (upward positive)

Design Strip: Support Line 7Design section Bending

MomentTwistingMoment

Axial Force NormalShear

InplaneShear

NormalShear Ecc

InplaneShear Ecc

kN-m kN-m kN kN kN mm mm701000 -4724.883 -4766.331 -481.048 -1913.809 1868.056 2047 1250701001 -5588.529 -3400.550 -456.337 -2324.698 1851.072 3164 1250701002 -5891.609 -5023.952 -399.702 -1288.109 1862.335 3404 1250701003 -7164.275 -2856.152 -611.493 -2204.474 2536.507 4476 1321701004 -7646.847 -2611.300 -692.160 -2973.303 3285.078 4653 1374702000 9774.197 -1974.781 -1296.405 13480.210 -1614.672 5236 1377

The starting point of a design section for identification of the centroid for vertical shear, as well as thelocation of the centroid of each design section is reported in Tables 152 of the Floor Pro report. Asample of this table is reproduced below:

152 DESIGN SECTION GEOMETRY

152.20 AUTOMATICALLY GENERATED DESIGN SECTIONSDesign Strip: Support Line 1

DesignSection

Start(x,y) End(x,y) Centroid(local x,z)

Area I Ytop Ybot

m m m mm2 mm4 mm mm101000 (-7.914,3.824) (-7.914,-0.161) (1.993,7.250) 9962800 5188900000000 1250 1250101001 (-7.407,3.801) (-7.407,-0.745) (2.273,7.250) 11364625 5919100000000 1250 1250101002 (-6.900,3.777) (-6.900,-1.230) (2.503,7.250) 12517475 6519500000000 1250 1250101003 (-6.900,3.777) (-6.900,-1.230) (2.503,7.250) 12517475 6519500000000 1250 1250