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1Composite Beam Theory Developed by Scott Civjan University of Massachusetts, Amherst

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Composite action accounts for the steel beam and floor slab working together to resist bending moments. Advantages over non-composite design: Increased strength Increased stiffness For given load conditions can achieve: Less steel required Reduced steel depth 2Composite Beam Theory Composite Beams

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Non-Composite Slip at Interface Two Neutral Axes M n = M nconcrete +M nsteel I=I concrete + I steel c c c T T NA Steel NA Composite NA Concrete T Fully Composite Assumed no slip at Interface One Neutral Axes M n >>M nconcrete +M nsteel I>>I concrete +I steel Shear at interface transferred by shear connectors. 3Composite Beam Theory Composite Behavior

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Composite Metal Deck Slabs – most commonly used today. Advantages: Stay in place form. Slab shoring typically not required. Metal deck serves as positive reinforcement. Metal deck serves as construction platform. Flat Soffit Slabs – typically, older construction. 4Composite Beam Theory Slabs

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b eff = effective width of the slab Function of: Span length Distance to nearest beam Distance to edge of slab s1s1 s2s2 s3s3 b eff edge 5Composite Beam Theory Effective Width of Slab b eff

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t s, slab thickness 6Composite Beam Theory b eff Flat Soffit Slabs

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7Composite Beam Theory b eff hrhr tctc Metal Deck Slab - Ribs Parallel to Beam Span A A h r =height of deck t c =thickness of concrete above the deck

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8Composite Beam Theory b eff hrhr A A Metal Deck Slab - Ribs Perpendicular to Beam Span tctc

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REFERENCES: COMPOSITE BEAMS Steel Deck Institute web pages Nelson Headed Studs web pages Steel Deck Manufacturer Catalogs These can be found on-line 9Composite Beam Theory

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Slab/Deck Span Girder Column Beam 10Composite Beam Theory Typical Framing PLAN

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INSERT PHOTOS: AISC Four Story Office Building Photo Slide Shows Metal Decking Slides Shear Studs Slides 11Composite Beam Theory

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Flexural Strength 12Composite Beam Theory

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Positive Moment The strength is determined as the plastic stress distribution on the composite section. Negative Moment It typically is assumed that the concrete carries no tensile forces and reinforcement is minimal, therefore strength is identical to a bare steel section. 13Composite Beam Theory Flexural Strength

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Fully Composite: The strength of either the floor slab in compression or the steel beam in tension is transferred at the interface. Partially Composite: The force transfer between the slab and beam is limited by the connectors. Positive Moment 14Composite Beam Theory Flexural Strength

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Lateral Torsional Buckling is prevented by the slab (continuous bracing). Local Flange Buckling is minimized by the slab. In general, strength is controlled by M p. 15Composite Beam Theory Flexural Strength Positive Moment

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INSERT INFORMATION: STRENGTH OF FULLY COMPOSITE BEAM SECTION CALCULATIONS Handout on Calculations: FullyCompositeCalcs.PDF 16Composite Beam Theory

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The bare steel section must support the temporary construction loads (before the concrete has set), or the steel beam must be shored until the composite section is effective. 17Composite Beam Theory Flexural Strength

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Shear Transfer Between Slab and Beam Typically, provided by headed shear studs. Shear flow, is calculated along the interface between slab and beam. Minimal slip allows redistribution of forces among shear studs. Therefore, studs are uniformly distributed along the beam. The total shear flow, must be provided on each side of M max. 18Composite Beam Theory

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19Composite Beam Theory Shear Transfer Between Slab and Beam Compression Force Tension Force

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20Composite Beam Theory Shear Transfer Between Slab and Beam Compression Force Tension Force

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21Composite Beam Theory Shear Transfer Between Slab and Beam = shear flow

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=shear flow to be transferred by shear studs V=Shear at the location considered Q=first moment of inertia of area above the interface I tr =moment of inertia of the transformed cross section 22Composite Beam Theory Shear Transfer Between Slab and Beam

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Consider when fully composite strength is greater than required. This may occur when: The shape is based on construction loads. The shape is based on architectural constraints. The lightest shape has excess strength. 23Composite Beam Theory Partially Composite Beam

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INSERT INFORMATION: STRENGTH OF PARTIALLY COMPOSITE BEAM SECTION CALCULATIONS Handout on Calculations: PartiallyCompositeCalcs.PDF 24Composite Beam Theory

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For composite section deflections: Transform section into equivalent steel section. Compute center of gravity of transformed section. Compute I tr of transformed section. 25Composite Beam Theory Serviceability

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26Composite Beam Theory b eff tctc hrhr Composite Beam b eff /n tctc hrhr Transformed Beam Serviceability Note: modular ratio, n = E s /E c

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It typically is assumed that the slab carries no shear forces, therefore composite strength is identical to that of a bare steel section. 27Composite Beam Theory Shear Strength

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28 Developed by Scott Civjan University of Massachusetts, Amherst

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Composite Beam - AISC Manual 14th Ed Chapter I: Composite Member Design 29

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Composite Beam - AISC Manual 14th Ed Slab effective width, b e To each side of the beam, b e is limited by: one-eighth beam span one-half distance to adjacent beam distance to edge of slab Lowest value controls. 30

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Composite Beam - AISC Manual 14th Ed Metal Deck Slab w r ≥ 2” t c ≥ 2” h r ≤ 3” 31 ≥1.5” ≥0.5” w r = average deck width h r =height of deck t c =thickness of concrete above the deck steel beam

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Composite Beam - AISC Manual 14th Ed Fully Composite Beam: Bending Strength 32

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Composite Beam - AISC Manual 14th Ed b = 0.90 ( b = 1.67) 33 Bending Strength

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Composite Beam - AISC Manual 14th Ed POSITIVE MOMENT For h/t w The strength is determined as the plastic stress distribution of the composite section. (*Note: All current ASTM A6 W, S and HP shapes satisfy this limit.) NEGATIVE MOMENT It is typically assumed that the concrete carries no tensile forces and reinforcement is minimal, therefore strength is identical to a bare steel section. 34 Bending Strength

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Composite Beam - AISC Manual 14th Ed INSERT INFORMATION: STRENGTH OF FULLY COMPOSITE BEAM SECTION CALCULATIONS Handout on Calculations: FullyCompositeCalcs.PDF 35

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Composite Beam - AISC Manual 14th Ed Fully Composite Strength can be determined by using Table 3-19. Y2 - Calculated per handout Y1 = 0 if PNA in the slab, Calculated per handout if PNA in the beam flange or web. 36 Bending Strength

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Composite Beam - AISC Manual 14th Ed Table 3-19 Nomenclature (Pg. 3-14) bebe a Y con a/2 Y2 Location of effective concrete flange force ( Q n ) TFL(pt.1) BFL(pt.5) 6 7 Y1 = Distance from top of steel flange to any of the seven tabulated PNA locations 4 Eq. spaces 1 2 3 4 5 TFL BFL tftf 37 Beam Flange Enlarged Detail 1 5

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Composite Beam - AISC Manual 14th Ed To reach fully composite strength, shear studs must transfer Q n for Y1 = 0 (maximum value) listed in Table 3-19. This is equivalent to value C* in calculations (handout). 38 Bending Strength

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Composite Beam - AISC Manual 14th Ed Shear Stud Strength 39

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Composite Beam - AISC Manual 14th Ed limits value to strength of individual shear studs. Strength of each stud, Q n Equation I8-1 limits value to crushing of concrete around the shear stud. 40

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Composite Beam - AISC Manual 14th Ed A sa =cross sectional area of shear stud E c =modulus of elasticity of concrete F u =shear stud minimum tensile strength (typically 65ksi) R g accounts for number of studs welded in each deck rib and w r /h r. Values are 1.0, 0.85 or 0.7. R p accounts for deck rib orientation with respect to the beam, stud engagement in the concrete above the rib, and weak or strong stud location. Values are 0.75 or 0.6. 41

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Composite Beam - AISC Manual 14th Ed Strength, Q n, for one shear stud Table 3-21 42

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Composite Beam - AISC Manual 14th Ed Limitations on shear stud placement for shear studs placed in metal decking: Center-Center Spacing:>4 times diameter ≤8 times slab thickness ≤36 inches Shear Stud Diameter:≤3/4” ≤2.5 times flange thickness unless over web 43

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Composite Beam - AISC Manual 14th Ed Composite strength requires that shear studs transfer Q n to each side of the maximum moment in the span. If Q n strength of the shear studs is inadequate to provide fully composite action, the beam is partially composite. 44

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Composite Beam - AISC Manual 14th Ed Partially Composite Beam: Bending Strength b = 0.90 ( b = 1.67) 45

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Composite Beam - AISC Manual 14th Ed INSERT INFORMATION: STRENGTH OF PARTIALLY COMPOSITE BEAM SECTION CALCULATIONS Handout on Calculations: PartiallyCompositeCalcs.PDF 46

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Composite Beam - AISC Manual 14th Ed Partially Composite Strength can be determined by using Table 3-19. Y1 - Calculated per handout 47 Y2 - Calculated per handout

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Composite Beam - AISC Manual 14th Ed Partially Composite Action is limited by the total strength of shear studs. Q n listed in Table 3-19. This is equivalent to value C* in calculations (handout). 48

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Composite Beam - AISC Manual 14th Ed Composite Beam: Shear Strength 49

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Composite Beam - AISC Manual 14th Ed SHEAR STRENGTH It typically is assumed that the slab carries no shear forces. Therefore, strength is identical to a bare steel section. 50

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Composite Beam - AISC Manual 14th Ed Composite Beam Deflection Calculations 51

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Composite Beam - AISC Manual 14th Ed Deflection Calculations Fully Composite I tr = transformed section moment of inertia Lower bound values of I tr are found in Table 3-20. Values assume concrete area equal to Q n /F y rather than actual area. 52

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Composite Beam - AISC Manual 14th Ed Deflection Calculations Partially Composite Equation C-I3-4 I eff = effective moment of inertia I s =moment of inertia of steel section only I tr =fully composite moment of inertia ΣQ nr =partially composite shear transfer C f =fully composite shear transfer 53

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Composite Beam - AISC Manual 14th Ed Deflection Calculations Partially Composite Equation C-I3-5 S eff = effective elastic section modulus S s =elastic section modulus of steel section only S tr =fully composite elastic section modulus ΣQ nr =partially composite shear transfer C f =fully composite shear transfer 54

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Composite Beam - AISC Manual 14th Ed Deflection Calculations Partially Composite Table 3-20 can be used for lower bound values of I eff. 55

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