CEE 323
Structural Steel
Design
Type of Member?
Tension?
Compresion?
Yeilding?
Rupture?
ϕt = 0.9
Ωt = 1.67
Pn = Fy*Ag
ϕt = 0.75
Ωt = 2.00
Pn = Fu*Ae
A992 Steel
Fy = 50ksi, Fu = 65ksi
Tension Design
LRFD
ASD
Pa ≤ Pn/Ωt
≤ 0.6FyAg
≤ 0.5FuAe
Pu ≤ ϕtPn
≤ 0.9FyAg
≤ 0.75FuAe
Table 1.1
Ag, Ix, Iy, rx,ry, weight, t
An = Ag - n(Ø+(1/16)+(1/16))t + Σ(s^2/4g)t
bn = b - n(Ø+(1/16)) + Σ(s^2/4g)t
Ae = AnU
Table D.3.1
Shear Lag Factor
U = 1 - x̄/l
l is the connection length
Block Shear
(J4-5)
choose smaller
Shear Yield + Tension Rupture
(0.6FuAnv+ UbsFuAnt)
Ubs = 1 for uniform tensile shear
Shear Rupture + Tension Rupture
(0.6FuAgv+ UbsFuAnt)
Buckling?
Inelastic Buckling
Lc/r ≤ 4.71√(E/Fy)
Elastic Buckling
4.71√(E/Fy) ≤ Lc/r
E = 29000 ksi
E = 199948 MPA
KL = Lc
√(Ix/A) = rx
√(Iy/A) = ry
Fcr = [(0.658)^(Fy/Fe)]Fy
Fcr = (0.877)Fe
AISC E-3-2
AISC 3-4
Fe = [π^2E]/[(Lc/r)^2]
Column Analysis
(given shape find strength)
Req. Strength ≤ Design Strength
Req. Strength ≤ Allowable Strength
Column Design
(given loads find shape)
What are the Loads?
What Type of Steel?
Effective Length?
Weak axis controls
Table 4.1a
Strong Axis Controls
Lc = Lcx/(rx/ry)
What are the shape Properties?
A, rx, ry, Lx, Ly
Effective Length Factor?
Single
Column?
Frame?
Table C-A-7.1
pin-pin = 1.0
pin-fixed = 0.7
fixed-fixed = 0.5
EQ C-A-3
G = [Σ(EI/L)col] / [Σ(EI/L)gird]
Max Slenderness Ratio?
Weak Axis Controls
Lcy/ry
Strong Axis Controls
Lcx/rx
What is Slenderness Limit?
4.71√(E/Fy)
Slenderness check for Fcr?
Inelastic Buckling
Lc/r ≤ 4.71√(E/Fy)
Fcr = [(0.658)^(Fy/Fe)]Fy
AISC E-3-2
Elastic Buckling
4.71√(E/Fy) ≤ Lc/r
Fcr = (0.877)Fe
AISC 3-4
Nominal Strength?
Pn = FcrAg
LRFD
Pu ≤ ϕcPn
ϕc = 0.9
ASD
Pa ≤ Pn/Ωc
Ωc = 1.67
AISC E3-2,3
Quick Fcr
Table 4-1a
Quick Design and Allowable Strength
given Lc
.
Critical Net Area is rupture path with the smallest An
min Ag?
Ag = Pu/ϕtFy
is min Ae > Pu/ϕtFu?
Ae = ϕtAg
what is min r?
min r > L/300
Pick trial Member based off mins
Check Slenderness
min r ≤ trial r
Aim for smallest/lightest member that meets structural design requirements
min Ag?
Ag = Pu/ΩtFy
is min Ae > Pu/ϕtFu?
Ae = ΩtAg
.