Basic Concepts. Introduction to Composite Design

Transcription

1 Introduction to Composite Design MORGAN STATE UNIVERSITY SCHOOL OF ARCHITECTURE AND PLANNING LECTURE IΧ Dr. Jason E. Charalambides Basic Concepts! What is a composite Beam? " Steel W-shape and portion of concrete slab acting together as a single unit to resist flexure It could be any combination of materials acting together to resist flexure, but most frequently the above mentioned materials are used. Image source: h.p:// (Image used strictly for educa;onal purposes) 2

2 Composite vs Noncomposite Behavior! Non-composite Beam: 3 Composite vs Noncomposite Behavior! Composite Beam: " Concrete and steel act as a single unit to resist flexure. " The flexural strength and the stiffness of a composite beam is much larger than the beam alone where the concrete slab only adds weight. 4

3 Composite vs Noncomposite Behavior! Full, vs partial Composite Interaction " Full: No slip at steel concrete interface. " Partial: Limited slip at interface. 5 Composite vs Noncomposite Behavior! Fully Composite Beam Design " Provide enough shear studs so that flexural strength is controlled by the full strength of steel and concrete working together. " Ideally there is no slip although a small amount of slip occurs at ultimate capacity.! Full, vs partial Composite Interaction " Flexural strength of beam is controlled by the strength of the shear studs. " Less studs required. " Significant slip is anticipated at the interface, even at normal service loads. For the course we will only address fully composite design 6

4 Composite vs Noncomposite Behavior! Full, vs partial Composite Interaction 7 Shored Vs Unshored Construction! Shored Construction " Steel beam is temporarily supported by shoring until the concrete is cast and cured (28 days). " Once the concrete is cured, steel and concrete work in tandem as one integrated unit.! Unshored Construction " Steel beam is not supported during the construction " Steel beam is acting by itself and has to have the strength too support the load of the wet concrete until it hardens. " Once concrete cures, it becomes an integral part of the composite element. The ultimate flexural strength of either is the same, and the most common method is that of unshored construction 8

5 Composite Beam Design Rules! The Effective Slab Width " The width of the slab may vary. However the contribution of the slab to the compression that is assumed by the composite element will not extend indefinitely. There is only a portion that can be considered as effective to that type of action. It can be determined as follows:! At the edge it will reach to the end of the slab,! Between beams it will reach half the distance between the centerlines of the beams,! It shall not exceed one eighth of the length of the beam. " Of the above mentioned conditions, the least governs 9 Effective Slab Width! Consider the scenario where the length of the beam is 34' and the distance between beams is 9': 10

6 Slab Thickness for Composite Design! Flat Soffit Slab: " Use of tc in strength calculations.! Formed Steel Deck Ribs Perpendicular to Beam " Use only tc in strength calculations. Concrete in ribs is neglected [AISC I3.2c(2)] 11 Slab Thickness for Composite Design! Formed Steel Deck Ribs Parallel to Beam " Concrete in ribs may be included in strength calculations [AISC I3.2c(3)] " Note: Concrete in ribs may be neglected with little reduction in strength 12

7 Flexural Strength Under Positive Moment! Flexure Element's Design Criteria Essentially a single criterion will suffice: And for +ve moment... Φ=0.9 ΦM n M u 13 Flexural Strength Under Positive Moment! Flexure Limit States " I. Beam Instability! Lateral Torsional Buckling " Prevented by the slab! Flange Local Buckling " Prevented by the slab! Web Local Buckling No Instability Limit State " Does not govern when: " Satisfied for all rolled W- Shapes with Fy 100ksi " II. Fully Plastic Cross Section 14

8 Procedure to Compute Nominal Moment for Fully Composite Beam! Assumptions: " Steel in Tension +F y " Steel in Compression +F y " Concrete in Tension 0 " Concrete in Compression f' c! Specified compressive strength of concrete (f' c ) varies and usually lies between 2 ksi & 5 ksi max. 15 Plastic Stress Distribution! Steel Beam alone M n = j d C= j d T =M p! Composite Beams M n = j d C= j d T =M p But, the N/A is not at the centerline. It needs to be located. 16

9 Computing Nominal Moment in a Slab!! b e = effective width of slab! d = depth of steel beam! h r = height of ribs! t c = thickness of concrete ribs 17 Computing Nominal Moment in a Slab! a being the depth of compression block in concrete, and A s area of steel C=(0.85 f ' c ) a b e a= A s F y t.85 f ' c b c e T =A s F y T =C 0.85 f ' c a b e =A s F y ΦM n =0.9 j d T =0.9 [ A s F y ] [ d 2 +h r +t c a 2 ] 18

10 Example! Steel Beam alone! Composite Beams 19 Example! Steel Beam alone! Composite Beams 20