STRUCTURES ARCHITECTURAL I: STATICS AND STRENGTH OF MATERIALS
ENDS 231
DR. ANNE NICHOLS FALL 2007
twenty two
LRFD design of steel beams
LRFD Beam Design 1 Lecture 22 Architectural Structures I ENDS 231 F2007abn
lecture
Load and Resistance Factor Design
loads on structures are
not constant can be more influential on failure happen more or less often UNCERTAINTY
i Ri Rn
factored load combination - resistance factor - load factors for types of loads (R)
Rn nominal strength
LRFD Beam Design 2 Lecture 22 Architectural Structures I ENDS 231 F2007abn
Load Types
D = dead load L = live load Lr = live roof load W = wind load S = snow load E = earthquake load R = rainwater load or ice water load
Architectural Structures I ENDS 231 F2007abn
LRFD Beam Design 3 Lecture 22
Load Combinations
ASCE-7 (2002)
summation means AND (combine)
1.4(D + F) 1.2(D + F + T)+ 1.6(L + H)+ 0.5(Lr or S or R) 1.2D + 1.6(Lr or S or R) + (L or 0.8W) 1.2D + 1.6W + L + 0.5(Lr or S or R) 1.2D + 1.0E + L + 0.2S 0.9D + 1.6W + 1.6H 0.9D + 1.0E + 1.6H
LRFD Beam Design 4 Lecture 22
Architectural Structures I ENDS 231
F2007abn
Steel Materials
ASTM A36 carbon
plates, angles Fy = 36 ksi & Fu = 58 ksi
ASTM A572 high strength low-alloy
some beams Fy = 60 ksi & Fu = 75 ksi
ASTM A992 for building framing
most beams Fy = 50 ksi & Fu = 65 ksi
LRFD Beam Design 5 Lecture 22 Architectural Structures I ENDS 231 F2007abn
Flexure
limit is in plastic stress range
i Ri = M u b M n = 0.9 Fy Z
Mu - maximum moment b - resistance factor for bending = 0.9 Mn - nominal moment (ultimate capacity) Fy - yield strength of the steel Z - plastic section modulus*
LRFD Beam Design 6 Lecture 22
Architectural Structures I ENDS 231
F2007abn
Internal Moments - at yield
material hasnt failed
I bh M y = fy = c 6
2
2
fy
2
b (2 c ) 2 bc = fy = 6 3
LRFD Beam Design 7 Lecture 22 Architectural Structures I ENDS 231
fy
F2007abn
Internal Moments - ALL at yield
all parts reach yield plastic hinge forms ultimate moment Atension = Acompression
Mp
= bc f y 3 = M y 2
2
Architectural Structures I ENDS 231
f fy = 50ksi E 1 y = 0.001724
LRFD Beam Design 8 Lecture 22
F2007abn
n.a. of Section at Plastic Hinge
cannot guarantee at centroid fyA1= fyA2 moment found from yield stress times moment area
M p = f y A1 d = f y Ai d i
n .a
LRFD Beam Design 9 Lecture 22 Architectural Structures I ENDS 231 F2007abn
Plastic Hinge Development
LRFD Beam Design 10 Lecture 22
Architectural Structures I ENDS 231
F2007abn
Plastic Hinge Examples
stability can be effected
LRFD Beam Design 11 Lecture 22
Architectural Structures I ENDS 231
F2007abn
Plastic Section Modulus
shape factor, k
k=
= 3/2 for a rectangle
M
p
My
S
p
1.1 for an I
k=Z
plastic modulus, Z
LRFD Beam Design 12 Lecture 22 Architectural Structures I ENDS 231
Z=
M
fy
F2007abn
Shear
i Ri = Vu vVn = 0.9(0.6 Fyw Aw )
Vu - maximum shear v - resistance factor for shear = 0.9 Vn - nominal shear Fyw - yield strength of the steel in the web Aw - area of the web = twd
LRFD Beam Design 13 Lecture 22
Architectural Structures I ENDS 231
F2007abn
Flexure Design
limit states for beam failure
1. 2. 3. 4. yielding lateral-torsional buckling* flange local buckling web local buckling
minimum Mn governs
i Ri = M u b M n
L...