1. Design of Bending Members in Steel

2. Steel wide flange beams in an office building

3. Composite Steel-Concrete Girders

4. An example of curved steel beams
German Historical Museum

5. Steel Girders for Bridge Decks
Sea to sky highway, Squamish

6. Cantilevered arms for steel pole

7. What can go wrong ? STEEL BEAMS: Bending failure
Lateral torsional buckling
Shear failure
Bearing failure (web crippling)
Excessive deflections

8. Bending Strength Linear elastic stresses Design Equation:y M
Design Equation:
Where Fb is the characteristic bending strength
For steel this is Fb = Fy
For timber it is Fb = fb (KDKHKSbKT)

9. Plastic moment capacity of steel beamsMy Fy Mp Fy C T a Ac At
Yield moment
Plastic moment
Which is the definition of the plastic section modulus Z
Z can be found by halving the cross-sectional area and multiplying the distance between the centroids of the two areas with one of the areas
This is also called the first moment of area
So, when do we use the one or the other ??

10. Steel beam design equation
For laterally supported beams (no lateral torsional buckling)
Mr =  Fy Z
for class 1 and 2 sections
Mr =  Fy S
for class 3 sections
where  = 0.9

11. Steel cross-section classes
Real thin plate sections
Will buckle before reaching Fy at extreme fibres
Mr < My
(Use Cold Formed Section Code S136)
Class 3
Fairly thin (slender) flanges and web
Will not buckle until reaching Fy in extreme fibres
Mr = My
Class 2
Stocky plate sections
Will not buckle until at least the plastic moment capacity is reached
Mr = Mp
Class 1
Very stockyplate sections
Can be bent beyond Mp and can therefore be used for plastic analysis

12. Load deflection curves for Class 1 to Class 4 sections

13. Local buckling of the compression flange

14. Local torsional buckling of the compression flange

15. Local web buckling

16. Lateral torsional buckling
Elastic buckling:
Mu = ωπ / Le √(GJ EIy ) + (π/L)2EIy ECw
Moment gradient factor
Torsional stiffness
Lateral bending stiffness
Warping stiffness Le x y Δx Δy θ

17. Moment resistance of laterally unsupported steel beams
Mr /  Mu
Mmax = My for class 3
or Mp for class 1 and 2
0.67Mmax
Mmax
1.15 Mmax [1- (0.28Mmax/Mu)] Le

18. Shear stress in a beam τ τ τmax τmax = V(0.5A)(d/4) ≈ V/Aw (bd3/12)by A b τ d
τmax
≈ V/Aw
=V/wd
b=w A
N.A. y τ d
τmax
= V(0.5A)(d/4)
(bd3/12)b
=1.5 V/A

19. Shear design of a steel I-beam
Vr = φ Aw 0.66 Fy
for h/w ≤ 1018/√Fy = 54.4 for 350W steel w
This is the case for all rolled shapes d h
For welded plate girders when
h/w ≥ 1018/√Fy
the shear stress is reduced to account for buckling of the web
(see clause )
Aw = d.w for rolled shapes and h.w for welded girders

20. Bearing failures in a steel beamk N
N+4t
N+10t w
Bearing failures in a steel beam
For end reactions
For interior reactions

21. Deflections A serviceability criterion Use unfactored loads
Avoid damage to cladding etc. (Δ ≤ L/180)
Avoid vibrations (Δ ≤ L/360)
Aesthetics (Δ ≤ L/240)
Use unfactored loads
Typically not part of the code Δ