1. Limit States Flexure Shear Deflection Fatigue Supports Elastic Plastic
Stability (buckling)
Shear
Deflection
Fatigue
Supports

2. Flexure
LRFD
ASD
Elastic
Plastic
Stability (buckling)

3. Flexure - Elastic
S=I/c : Section Modulus (Tabulated Value)

4. Flexure - Plastic

5. Mp = Acfy = Atfy = fy (0.5A) a = Mp=Zfy
Flexure - Plastic
C=T
Acfy=Atfy
Ac=At
Mp = Acfy = Atfy = fy (0.5A) a = Mp=Zfy
Mp/ My =Z/S
For shapes that are symmetrical about the axis of bending the plastic and elastic neutral axes are the same
Z=(0.5A)a : Plastic Section Modulus (Tabulated Value)

6. Flange Local Buckling (FLB) Elastically or Inelastically
Flexure - Stability
A beam has failed when:
Mp is reached and section becomes fully plastic Or
Flange Local Buckling (FLB) Elastically or Inelastically
Web Local Buckling (WLB) Elastically or Inelastically
Lateral Torsional Buckling (LTB) Elastically or Inelastically

7. Lb Flexure - Stability Slenderness Parameter FLB l=bf/2tf WLB l=h/tw
LTB
l= Lb /ry tf bf tw h Lb

8. FLB and WLB (Section B5 Table B4.1)
Flexure - Stability
FLB and WLB (Section B5 Table B4.1)
Evaluate Moment Capacity for Different l
Compact
Non
Slender Mp Mr lp lr
FLB
l=bf/2tf
WLB
l=h/tw

9. Slenderness Parameter - Limiting Values
AISC B5 Table B4.1 pp

10. Slenderness Parameter - Limiting Values
AISC B5 Table B4.1 pp

11. Slenderness Parameter - Limiting Values
AISC B5 Table B4.1 pp

12. FLB and WLB (Section B5 Table B4.1)
Flexure - Stability
FLB and WLB (Section B5 Table B4.1)
Compact
Non
Slender Mp Mr lp lr
FLB
l=bf/2tf
WLB
l=h/tw

13. Bending Strength of Compact Shapes
Lateral Torsional Buckling

14. Bending Strength of Compact Shapes

15. Bending Strength of Compact Shapes
Laterally Supported Compact Beams

16. Bending Strength of Compact Shapes

17. Bending Strength of Compact Shapes
Elastic Buckling

18. Elastic Buckling
Cb = factor to account for non-uniform bending within the unbraced length
See AISC table 3-1 p 3.10
Mmax A B C
L/4
L/4
L/4
L/4

19. Elastic Buckling

20. Elastic Buckling

21. Elastic Buckling
Cb = factor to account for non-uniform bending within the unbraced length
Rm= 1 for doubly symmetric cross sections and singly symmetric subject to single curvature

22. Elastic Buckling
Cb = factor to account for non-uniform bending within the unbraced length

23. Elastic Buckling
Cb = factor to account for non-uniform bending within the unbraced length
ho = distance between flange centroids = d-tf

24. Bending Strength of Compact Shapes

25. Bending Strength of Compact Shapes
Inelastic Buckling
Linear variation between Mp and Mr

26. Nominal Flexural Strength – Compact Shapes

27. Nominal Flexural Strength – NON-Compact Shapes
Most W- M- S- and C- shapes are compact
A few are NON-compact
NONE is slender
Webs of ALL hot rolled shapes in the manual are compact
FLB and LTB
Built-Up welded shapes can have non-compact or slender webs
FLB, WLB, LTB (AISC F4 and F5)

28. Nominal Flexural Strength – NON-Compact Shapes
WLB

29. Design of Beams - Limit States
Flexure
Elastic
Plastic
Stability (buckling)
Shear
Deflection

30. Design for Shear Large concentrated loads placed near beam supports
Rigid connection of beams and columns with webs on the same plane
Notched or coped beams
Heavily loaded short beams
Thin webs in girders

31. Design for Shear V: Vertical shear at the section under consideration
Q: First moment about of neutral axis of area of the cross section between point of interest and top or bottom of section (depends on y)
I: Moment of inertia of section
b: width of section at point of interest

32. Web fails before flanges
Design for Shear
Small width b
d/b=2 Error ~3%
d/b=1 Error ~12%
d/b=1/4 Error 100%
Web fails before flanges
Average Shear Stress
Nominal Strength if no buckling:

33. Design for Shear h/tw Failure of Web due to Shear: Yielding
Inelastic Buckling
Elastic Buckling
h/tw>260 Stiffeners are required
Appendix F2

34. Design for Shear AISC Specs G pp 16.1-64
Shear Strength must be sufficient to satisfy
LRFD
resistance factor for shear=0.9
maximum shear based on the controlling combination for factored loads
nominal shear strength
depends on failure mode
ASD
maximum shear based on the controlling combination for service loads
Safety factor

35. AISC Spec requirements for Shear
Cv depends on whether the limit state is web yielding, web inelastic buckling or web elastic buckling

36. AISC Spec requirements for Shear
Special Case for Hot Rolled I shapes with
Most W shapes with

37. AISC Spec requirements for Shear Chapter G
All other doubly and singly symmetric shapes except round HSS

38. DEFLECTIONS AISC Specs Chapter L
Serviceability Limit State
Limiting Value
Deflections due to Service Loads
<
Governing Building Code, IBC etc
Use deflection formulas in AISC Part 3 Or standard analytical or numerical methods
Calculate due to UNFACTORED (service) loads

39. Shear is rarely a problem in rolled steel beams usual practice
Design
Shear is rarely a problem in rolled steel beams
usual practice
Design for Flexure and Check for Shear and Deflections Or
Design for Deflections and Check for Flexure and Shear

40. Design Compute Required Moment Strength Mu or Ma
Weight of Beam can be assumed and verified or ignored and checked after member is selected
Select shape that satisfies strength requirements
Assume shape, compute strength, compare with required, revise if necessary or
Use beam design aids in Part 3 of the Manual
Check Shear and deflections