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**Advanced Flexure Design COMPOSITE BEAM THEORY SLIDES**

Teaching Modules for Steel Instruction Advanced Flexure Design COMPOSITE BEAM THEORY SLIDES Developed by Scott Civjan University of Massachusetts, Amherst Composite Beam Theory

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Composite Beams 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 Composite Beam Theory

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**Composite Behavior c T T c c NA NA Concrete Composite T NA Steel**

Non-Composite Slip at Interface Two Neutral Axes Mn= Mnconcrete+Mnsteel I = Iconcrete + Isteel Fully Composite Assumed no slip at Interface One Neutral Axes Mn >> Mnconcrete+Mnsteel I >> Iconcrete+Isteel Shear at interface transferred by shear connectors. Composite Beam Theory 3

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**Slabs 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. Composite Beam Theory

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**Effective Width of Slab**

beff = effective width of the slab Function of: Span length Distance to nearest beam Distance to edge of slab beff beff s3 edge s1 s2 edge Composite Beam Theory

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Flat Soffit Slabs beff ts, slab thickness Composite Beam Theory

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**A A Metal Deck Slab - Ribs Parallel to Beam Span beff hr tc**

hr = height of deck tc = thickness of concrete above the deck Composite Beam Theory 7 7

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**A A Metal Deck Slab - Ribs Perpendicular to Beam Span beff hr tc**

Composite Beam Theory

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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 Composite Beam Theory

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**Typical Framing Column Girder Beam Slab/Deck Span PLAN**

Composite Beam Theory

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**INSERT PHOTOS: AISC Four Story Office Building Photo Slide Shows**

Metal Decking Slides Shear Studs Slides Composite Beam Theory

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Flexural Strength Composite Beam Theory

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**Flexural Strength 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. Composite Beam Theory

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**Flexural Strength Positive Moment**

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. Composite Beam Theory

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**Flexural Strength Positive Moment**

Lateral Torsional Buckling is prevented by the slab (continuous bracing). Local Flange Buckling is minimized by the slab. In general, strength is controlled by Mp. Composite Beam Theory

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**Handout on Calculations:**

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

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Flexural Strength 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. Composite Beam Theory

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**Shear Transfer Between Slab and Beam**

Typically, provided by headed shear studs. Shear flow, n, 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, n, must be provided on each side of Mmax. Composite Beam Theory

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**Shear Transfer Between Slab and Beam**

Compression Force Tension Force Composite Beam Theory 19 19

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**Shear Transfer Between Slab and Beam**

Compression Force Tension Force Composite Beam Theory 20 20

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**Shear Transfer Between Slab and Beam**

n = shear flow Composite Beam Theory 21 21

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**Shear Transfer Between Slab and Beam**

= shear flow to be transferred by shear studs V = Shear at the location considered Q = first moment of inertia of area above the interface Itr = moment of inertia of the transformed cross section Composite Beam Theory

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**Partially Composite Beam**

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. Composite Beam Theory

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**Handout on Calculations:**

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

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**Serviceability For composite section deflections:**

Transform section into equivalent steel section. Compute center of gravity of transformed section. Compute Itr of transformed section. Composite Beam Theory

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**Serviceability beff beff/n tc tc hr hr Composite Beam Transformed Beam**

Note: modular ratio, n = Es/Ec Composite Beam Transformed Beam Composite Beam Theory 26 26

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

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**AISC Manual -14th Edition**

Teaching Modules for Steel Instruction Advanced Beam Design COMPOSITE BEAM AISC Manual -14th Edition Developed by Scott Civjan University of Massachusetts, Amherst

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

Metal Deck Slab ≥0.5” tc ≥ 2” ≥1.5” hr ≤ 3” wr ≥ 2” steel beam wr = average deck width hr = height of deck tc = thickness of concrete above the deck Composite Beam - AISC Manual 14th Ed 31 31

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

fb = 0.90 (Wb = 1.67) Bending Strength Composite Beam - AISC Manual 14th Ed

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**Composite Beam - AISC Manual 14th Ed**

Bending Strength POSITIVE MOMENT For h/tw 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. Composite Beam - AISC Manual 14th Ed

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

Bending Strength 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. Composite Beam - AISC Manual 14th Ed

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

Shear Stud Strength Composite Beam - AISC Manual 14th Ed

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**Composite Beam - AISC Manual 14th Ed**

Strength of each stud, Qn Equation I8-1 limits value to crushing of concrete around the shear stud. limits value to strength of individual shear studs. Note that this indicates that push-out of a stud through a rib could be minimized by increasing Fu of the stud, which is not realistic. The equations assume standard materials. Composite Beam - AISC Manual 14th Ed

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**Composite Beam - AISC Manual 14th Ed**

Asa = cross sectional area of shear stud Ec = modulus of elasticity of concrete Fu = shear stud minimum tensile strength (typically 65ksi) Rg accounts for number of studs welded in each deck rib and wr/hr. Values are 1.0, 0.85 or 0.7. Rp 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. Composite Beam - AISC Manual 14th Ed

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**Strength, Qn, for one shear stud Table 3-21**

Composite Beam - AISC Manual 14th Ed

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**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 Composite Beam - AISC Manual 14th Ed

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

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

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**Composite Beam - AISC Manual 14th Ed**

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

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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. Composite Beam - AISC Manual 14th Ed

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**Composite Beam - AISC Manual 14th Ed**

Deflection Calculations Composite Beam - AISC Manual 14th Ed

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**Deflection Calculations**

Fully Composite Itr = transformed section moment of inertia Lower bound values of Itr are found in Table 3-20. Values assume concrete area equal to SQn/Fy rather than actual area. Composite Beam - AISC Manual 14th Ed

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**Deflection Calculations**

Partially Composite Equation C-I3-4 Ieff = effective moment of inertia Is = moment of inertia of steel section only Itr = fully composite moment of inertia ΣQnr= partially composite shear transfer Cf = fully composite shear transfer Composite Beam - AISC Manual 14th Ed

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**Deflection Calculations**

Partially Composite Equation C-I3-5 Seff = effective elastic section modulus Ss = elastic section modulus of steel section only Str = fully composite elastic section modulus ΣQnr= partially composite shear transfer Cf = fully composite shear transfer Composite Beam - AISC Manual 14th Ed

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**Deflection Calculations**

Partially Composite Table 3-20 can be used for lower bound values of Ieff. Composite Beam - AISC Manual 14th Ed

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