1. Design of Thin-Walled Members

2. Various shapes of cold-formed sections

10. Advantages Lightness High strength and stiffness
Ease of prefabrication and mass production
Fast and easy erection and installation
Substantial elimination of delays due to weather
More accurate detailing
Non shrinking and non creeping at ambient temperatures
Formwork unneeded
Termite-proof and rot proof
Uniform quality
Economy in transportation and handling
Non combustibility
Recyclable material

11. Characteristic Behavior
relatively high width to thickness ratios.
Un-stiffened or incompletely restrained parts of sections.
singly symmetrical or unsymmetrical shapes.
geometrical imperfections of the same order as or exceeding the thickness of the section.
structural imperfections caused by the cold-forming process.

12. Characteristic Behavior
buckling within the range of large deflections.
effects of local buckling on overall stability.
combined torsional and flexural buckling.
shear lag and curling effects.
effects of varying residual stresses over the section.

13. Materials
For cold-formed sections and sheeting it is preferable to use cold-rolled continuously galvanized steel with yield stresses in the range of N/mm2, and with a total elongation of at least 10%

14. ASD (Allowable Stress Design) Method

15. LRFD (Load and Resistance Factor Design) Method

16. Safety Factors and Resistance Factors

17. Nominal Loads

18. Effects of Cold Forming
As cold forming involves work hardening effects, the yield stress, the ultimate strength and the ductility are all locally influenced by an amount which depends on the bending radius, the thickness of the sheet, the type of steel and the forming process.
The average yield stress of the section then depends on the number of corners and the width of the flat elements

19. Effects of Cold Forming
The average yield stress can be estimated by approximate expressions given in the appropriate codes. In the example, the average yield stress ratio fya/fyb» 1,05 and the corner yield stress ratio fyc/fyb» 1,4.

20. Effects of Cold Forming
full-section tensile yield strength;

21. The effective width concept

22. Effective Cross-sections
evaluate the effective width of the compression elements of the section
calculate the geometric properties of the effective section
the design procedure is the same as for thick-walled sections
the resistance of a thin-walled effective cross-section is limited by the design yield stress at any part of the section, based on an elastic analysis.
the design resistance is based on the value fy/M, where  M is a partial safety factor for resistance (normally M=1,1).

23. Validity of the effective width concept

24. Effective Section
Uniformly compressed stiffened and unstiffened elements
w = the flat width;
ρ = the reduction factor
λ = a slenderness factor
f = the stress in the element
k = the buckling factor
= 4 for stiffened Elements
= 0.43 for unstiffened element

25. Effective Section
Uniformly compressed stiffened and unstiffened elements

26. Effective Section w = the flat width; ρ = the reduction factor
checking the serviceability state of uniformly compressed elements supported by webs on both edges:
w = the flat width;
ρ = the reduction factor
λ = a slenderness factor
f = the stress in the element
k = the buckling factor
= 4 for stiffened Elements
= 0.43 for unstiffened element

27. Effective Section Ψ = f2/f1 b = the effective width (uniformly
Webs and stiffened elements with stress gradient
Ψ = f2/f1
b = the effective width (uniformly
compressed stiffened elements) with f1 substituted by f and with k determined from
k=4+2(1–ψ)3+2(1–ψ)

28. Doubly supported element

29. Singly supported element

30. Effective Section
Unstiffened elements and edge stiffened with stress gradient
In this case, the code suggests evaluating the effective widths in accordance with Section (uniformly compressed unstiffened elements) using a uniform distribution with the maximum value of stress f.

31. Effective Section
Uniformly compressed elements with one intermediate stiffener
Uniformly compressed elements with an edge stiffener

32. Limits for b/t ratios The design rules give limits for b/t ratios as.
These maximum width-to-thickness ratios depend partly on limited experimental evidence, and partly on experience from manufacturing and handling sections

33. Resistance vs. geometrical properties.

34. RESISTANCE OF CROSS-SECTIONS
LRFD Factored resistance фRn
Resistance under axial tension
Resistance under axial compression
Resistance under bending moment
Combined axial tension and bending
Combined axial compression and bending
Combined shear force and bending moment
Buckling resistance under axial compression
Buckling resistance under axial compression and bending

35. Resistance under axial tension - LRFD
The nominal tensile strength Tn shall be determined as follows
An = the net area of the cross-section;
Fy = the design yield stress, which takes into account the increase in basic yield strength due to strain-hardening
Фt = resistance reduction factor

36. Resistance under axial compression - LRFD
Assuming that the member is not subject to the risk of axial buckling,
the nominal compression strength Pn shall be determined as follows
Ae = the effective area at the stress Fy;
Fy = the design yield stress
Фt = resistance reduction factor

37. Resistance under bending moment - LRFD
The nominal flexural strength Mn shall be determined as follows:
for sections with unstiffened compression flange
Se = the elastic section modulus of the effective section, calculated for extreme compression or tension fiber at Fy;
Fy = the design yield stress—for the section to be fully effective it should take into account the increase of the basic yield strength due to strain-hardening.
Фb = resistance reduction factor

38. Combined axial tension and bending - LRFD
The required strengths T, Mx, My shall satisfy the following equations
T = the required tensile axial strength;
Tn = the nominal tensile axial strength
Mx, My = the required flexural strengths about the centroidal axes;
Mnx, Mny = the nominal flexural strengths about the centroidal;
Mnxt = SfxtFy Mnyt = SfytFy
Sfxt = the elastic section modulus of the full unreduced section for the extreme tension fibre about the x axis;
Sfyt=the elastic section modulus of the full unreduced section for the extreme tension fibre about the y axis;
фb, фt=are the appropriate safety factors.

39. Combined axial compression and bending - LRFD
If the member is not subject to the risk of axial buckling, the required strengths P, Mx, My shall satisfy the following equations,
P = the required compressive axial strength;
Pn = the nominal axial strength
Mx, My = the required flexural strengths with respect to the centroidal axes of the effective section determined for the required cornpressive axial strength alone;
Mnx, Mny = the nominal flexural strengths about the centroidal axes;
фb, фc = the appropriate safety factors.

40. Buckling resistance under axial compression - LRFD
Ae = the effective area at the stress Fn;
Fe = the smallest value for the elastic flexural, torsional and torsional-flexural buckling
stress. (the case here is for elastic flexural buckling)
E is the modulus of elasticity,
K is the effective length factor
L is the unbraced length
r is the radius of gyration of the full, unreduced section.
Фt = resistance reduction factor
The nominal axial strength Pn shall be calculated as follows
for λc≤1.5
for λc>1.5

41. Buckling resistance under axial compression - LRFD

42. Buckling resistance under axial compression and bending - LRFD
The required strengths P, Mx, My shall satisfy the following equations
P = the required compressive axial strength;
Pn = the nominal axial strength;
Pno = the nominal axial strength (i.e. with Fn=Fy);
Mx, My = the required flexural strengths with respect to the centroidal axes of the effective section determined for the required compressive axial strength alone;
Mnx, Mny = the nominal flexural strengths about the centroidal axes
фb, фc = are the appropriate safety factors

43. Buckling resistance under axial compression and bending - LRFD
The reduction coefficient α is given by:
Ix, Iy=the moments of inertia of the full unreduced section about the x axis and y axis,
respectively;
Lx, Ly=the actual unbraced lengths for bending about the x axis and y axis,

44. Buckling resistance under axial compression and bending - LRFD
Kx, Ky = the effective length factors for buckling about the x and y axes,
Cmx, Cmy=coefficients defined as follows:
Cm=0.85 for compression member in frames subject to joint translation (sideways);
Cm=0.6–0.4M1/M2 for restrained compression members in frames braced against joint translation and not subjected to transverse loading between their supports in the plane of bending (M1/M2 is the ratio of the smaller to the larger moment at the end of the
member);
Cm= 0.85 for compression members in frames braced against joint translation and subjected to transverse loading between their supports in the plane of bending, when their ends are restrained;
Cm=1.00 for compression members in frames braced against joint translation and subjected to transverse loading between their supports in the plane of bending, when their ends are not restrained.