14-Design of Beam (Steel Structural Design & Prof. Shehab Mourad)

1. 1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
sDesign of Beam
Bending stresses in beams-1
My = Yield moment
= (C or T) yc.t
= Fy. S
where S : Elastic modulus
For rectangular section S = bd2
/6
Mp = Plastic moment
= (C or T ) yc.t
= Fy . Z
Where Z : Plastic modulus
For rectangular section Z = bd2
/4
Mp = Z for rectangular section Z = 1.5
My S S
For W shapes Z/S ≈ 1.10 → 1.15
M
Curvature Φ
1
2
3
4 5
M p
M y
Pu Plastic hingeW shape
Area of yielding
ε t
ε c
-
+Φ
Strain diagramBeam cross section
f < Fy
f < Fy
Fy
Fy Fy
Fy
Fy
Fy
Fy
Fy
+ + + + +
- - - - -
1 2 3 4 5

2. 2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
2- Effect of beam unbraced length on its moment capacity
Buckling of the compression flange of the beam can occur if the unbraced
length of the compression flange ( Lb) exceeds certain values
Lp : Is the largest value of unbraced length that Mp can be reached
Lr : is the largest value of unbraced length that cause inelastic torsional
buckling

3. 3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
3 - Beam bending strength
Resistance factor for flexural (Φ) = 0.90
(a) if Lb ≤ L p (Zone 1)
Φ Mn = least of Φ Mp
Φ 1.5 Fy . S
(b) if Lp < Lb ≤ Lr (Zone 2) (inelastic lateral torsional buckling)
Φ Mn = Φ Cb [ Mp – ( Mp – Mr) (Lb - Lp) ] ≤ Φ Mp
(Lr – Lp)
= Φ Cb [ Mp – BF (Lb - Lp) ] ≤ Φ Mp
Where, Lp, Lr, Mp, Mr, BF are obtained from LRFD tables
Cb : is a modification factor for non-uniform moment diagram
( c ) if Lb > Lr (Zone 3) ( Elastic lateral torsional buckling)
Φ Mn = Φ Cb Mcr
Where Mcr is the critical moment at which the beam will twist elastically
due to the elastic buckling of the compression flange, its values are obtained
from graphs