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

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

3. 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

4. - - - - + 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

5. 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

6. 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)