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Course: ENDS 231, Fall 2008School: Texas A&M
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STRUCTURES ARCHITECTURAL I: STATICS AND STRENGTH OF MATERIALS ENDS 231 DR. ANNE NICHOLS SUMMER 2006 nineteen LRFD design of steel beams LRFD Beam Design 1 Lecture 19 Architectural Structures I ENDS 231 Su2006abn 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 -...
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STRUCTURES ARCHITECTURAL I: STATICS AND STRENGTH OF MATERIALS
ENDS 231
DR. ANNE NICHOLS SUMMER 2006
nineteen
LRFD design of steel beams
LRFD Beam Design 1 Lecture 19 Architectural Structures I ENDS 231 Su2006abn
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 S2006abn
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 S2006abn
LRFD Beam Design 3 Lecture 22
Load Combinations
"summation" means AND (combine)
1.4D 1.2D + 1.6L + 0.5(Lr or S or R) 1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W) 1.2D + 1.3W + 0.5L + 0.5(Lr or S or R) 1.2D + 1.5E + (0.5L or 0.2S) 0.9D - (1.3W or 1.5E)
LRFD Beam Design 4 Lecture 22
Architectural Structures I ENDS 231
S2006abn
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 S2006abn
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
S2006abn
Internal Moments - at yield
material hasn't 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
S2006abn
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 I Structures ENDS 231
f fy = 50ksi E 1 y = 0.001724
LRFD Beam Design 8 Lecture 22
S2006abn
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 S2006abn
Plastic Hinge Development
LRFD Beam Design 10 Lecture 22
Architectural Structures I ENDS 231
S2006abn
Plastic Hinge Examples
stability can be effected
LRFD Beam Design 11 Lecture 22
Architectural Structures I ENDS 231
S2006abn
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
S2006abn
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
S2006abn
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
LRFD Beam...
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SID 22 35 356 541 941 1266 1395 1418 1559 1609 1623 1623 1868 2218 2507 2836 3504 3577 3730 3747 3838 3923 3997 4237 4425 4809 4983 5265 5332 5469 5486 5490 5849 6000 6417 6742 6808 7211 7231 7460 7499 7578 8316 8384 8511 8594 8595 8638 9054 9357 945
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SID 22 35 356 541 941 1266 1395 1418 1559 1609 1623 1623 1868 2218 2507 2836 3504 3577 3730 3747 3838 3923 3997 4237 4425 4809 4983 5265 5332 5469 5486 5490 5849 6000 6417 6742 6808 7211 7231 7460 7499 7578 8316 8384 8511 8594 8595 8638 9054 9357 945
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SID 0022 0035 0356 0541 0941 1266 1395 1418 1553 1559 1609 1623 1623 1682 1868 2165 2218 2410 2507 2670 2836 3324 3412 3504 3577 3730 3747 3838 3923 3997 4237 4250 4308 4425 4809 4983 5265 5332 5335 5469 5486 5490 5849 6000 6279 6402 6417 6742 6808 7
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SID 0022 0035 0356 0541 0941 1266 1395 1418 1553 1559 1609 1623 1623 1682 1868 2165 2218 2410 2507 2670 2836 3324 3412 3504 3577 3730 3747 3838 3923 3997 4237 4250 4308 4425 4809 4983 5265 5332 5335 5469 5486 5490 5849 6000 6279 6402 6417 6742 6808 7
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SID 22 35 356 541 941 1266 1395 1418 1553 1559 1609 1623 1623 1682 1868 2165 2218 2507 2670 2836 3324 3412 3504 3577 3730 3747 3838 3923 3997 4237 4425 4809 4983 5265 5332 5469 5486 5490 5849 6000 6417 6742 6808 7211 7214 7231 7460 7499 7578 8316 838
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SID 0022 0035 0356 0541 0941 1266 1395 1418 1559 1609 1623 1623 1868 2218 2507 2836 3504 3577 3730 3747 3838 3923 3997 4237 4425 4809 4983 5265 5332 5469 5486 5490 5849 6000 6417 6742 6808 7211 7231 7460 7499 7578 8316 8384 8511 8594 8595 8638 9054 9
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SID 22 35 356 541 941 1266 1395 1418 1559 1609 1623 1623 1868 2218 2507 2836 3504 3577 3730 3747 3838 3923 3997 4237 4425 4809 4983 5265 5332 5469 5486 5490 5849 6000 6417 6742 6808 7211 7231 7460 7499 7578 8316 8384 8511 8594 8595 8638 9054 9357 945
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SID 22 35 356 541 941 1266 1395 1418 1553 1559 1609 1623 1623 1682 1868 2165 2218 2507 2670 2836 3324 3412 3504 3577 3730 3747 3838 3923 3997 4237 4425 4809 4983 5265 5332 5469 5486 5490 5849 6000 6417 6742 6808 7211 7214 7231 7460 7499 7578 8316 838
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SID 22 35 356 541 941 1266 1395 1418 1553 1559 1609 1623 1623 1682 1868 2165 2218 2507 2670 2836 3324 3412 3504 3577 3730 3747 3838 3923 3997 4237 4250 4425 4809 4983 5265 5332 5469 5486 5490 5849 6000 6402 6417 6742 6808 7211 7214 7231 7460 7499 757
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