Design of Steel Structures (2) Design of Steel Beams

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Presentation transcript:

Design of Steel Structures (2) Design of Steel Beams Prof. D. Ahmed Mohamed Anwar Lecture 1

Common Beam Cross Sections S.I.P or I.P.E Channel B.F.I. Built up sections Built up sections

Performance and Behavior of Steel Beams: The behavior of a beam under Concentrated Load at mid-span illustrated by the following example. The max. moment, outer - fiber strain and stresses occur at mid-span Successive Stages in bending are shown in This figure . (I) Elastic Range [Stage (1) and Stage (2)] (II) Plastic Range [Stage (3) and Stage (4)] P 3 2 4 1 (a) 3 2 4 1 (b) My Mp Fy (c) Y ε1<εy ƒ1<Fy Ε1=εy ƒ1=Fy Fy - - (d) X X M=My Fy + + (e) Stage 1 Stage 2 Y (I) Elastic Range

- - - - + Variation in Strain and Stress Along The Depth of the Beam 2 Strength in Elastic Range = My = Fy *Sx , Zx = elastic Section Modulus Strength in Plastic Range = My = Fy *Sp , Zp = Plastic Section Modulus , and, ζ =(Mp/My) = (Zx/Zp) = 1.1 – 1.18 For I- Sections and = 1.5 for Rectangular Section M=My M=Mp Y ε1<εy ƒ1<Fy ε1=εy ƒ1=Fy ε1>εy ƒ1=Fy ε1>>εy ƒ1=Fy - - - - X + + + + Stage 1 Stage 2 Stage 3 Stage 4 Y (I) Elastic Range (II) Plastic Range Variation in Strain and Stress Along The Depth of the Beam Stress (σ) Elastic Range Plastic Range Strain Hardening Idealized Stress – Strain Diagram 2 3 4 Fy 1 ƒ1 Strain (ε) ε1 ε4 ε2 ε3 εy

Fully Laterally Supported Beams (Floor or Roof Beams) Flexural Members have the Compression Flange Restrained to Satisfy Lateral Support . This is True in Beams Supporting floors and Roofs, where the beam is in direct contact or has the top Flange embedded in the floor or Roof Slabs as the Following: LUact =0.0 R. C. Slab Shear Connector Steel Section imbedded in Concrete Section Top Flange embedded in Concrete Slab Top Flange Connected with R. C. Slab by Shear Connectors Composite Slab Box Girder R. C. Slab Beam is Laterally Supported by Composite Slab

Laterally Unsupported Beams Torsion will be combined with Bending when the Line of action of Load is not passing through the Shear Center of the cross section P S U M M (I) A B C D P V X S Y (II) L1 L2 L3 Φ A B D C Section S-S Main Beam “A-D” provided by Lateral Supported by Lateral Beams at B & C “Buckling of Beams Provided with Lateral Secondary Beams” LU act =Greater (L1, L2 & L3)