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Course: ENDS 231, Fall 2008School: Texas A&M
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Word Count: 555
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STRUCTURES ARCHITECTURAL I: STATICS AND STRENGTH OF MATERIALS ENDS 231 DR. ANNE NICHOLS SPRING 2008 twenty one beams: deflection & design Beam Deflection & Design 1 Lecture 21 Architectural Structures I ENDS 231 S2008abn lecture Design for Strength +... strength design forces & material serviceability limit deflection and cracking control noise & vibration no excessive...
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STRUCTURES ARCHITECTURAL I: STATICS AND STRENGTH OF MATERIALS
ENDS 231
DR. ANNE NICHOLS SPRING 2008
twenty one
beams: deflection & design
Beam Deflection & Design 1 Lecture 21 Architectural Structures I ENDS 231 S2008abn
lecture
Design for Strength +...
strength design
forces & material
serviceability
limit deflection and cracking control noise & vibration no excessive settlement of foundations durability appearance component damage ponding
Beam Deflection & Design 2 Lecture 21 Architectural Structures I ENDS 231 S2008abn
Beam Deformations
curvature relates to
bending moment modulus of elasticity moment of inertia
1 M = R EI
c
R
L
y
Beam Deflection & Design 3 Lecture 21
Architectural Structures I ENDS 231
M ( x) curvature = EI M ( x) = slope = dx EI M ( x) = deflection = dx EI
S2008abn
Deflected Shape & M(x)
-M(x) gives shape indication boundary conditions must be met
Beam Deflection & Design 4 Lecture 21
Architectural Structures I ENDS 231
S2008abn
Boundary Conditions
at pins, rollers, fixed supports: y = 0 at fixed supports: = 0 at inflection points from symmetry: = 0 ymax at
Beam Deflection & Design 5 Lecture 21
dy =0 dx
Architectural Structures I ENDS 231 S2008abn
Superpositioning
if w can be superpositioned
& y can elastic range only!
+ =
Beam Deflection & Design 6 Lecture 21
Architectural Structures I ENDS 231
S2008abn
Deflection Limits
based on service condition, severity
Use LL only Roof beams: Industrial L/180 Commercial plaster ceiling L/240 no plaster L/360 Floor beams: Ordinary Usage L/360 Roof or floor (damageable elements)
Beam Deflection & Design 7 Lecture 21 Architectural Structures I ENDS 231
DL+LL L/120 L/180 L/240 L/240 L/480
S2008abn
Lateral Buckling
lateral buckling caused by compressive forces at top coupled with insufficient rigidity can occur at low stress levels stiffen, brace or bigger Iy
Beam Deflection & Design 8 Lecture 21
Architectural Structures I ENDS 231
S2008abn
Local Buckling
steel I beams flange
in buckle direction of smaller radius of gyration
web
force crippling
Beam Deflection & Design 9 Lecture 21 Architectural Structures I ENDS 231 S2008abn
Local Buckling
web flange
Beam Deflection & Design 10 Lecture 21
Architectural Structures I ENDS 231
S2008abn
Shear in Web
panels in plate girders or webs with large shear buckling in compression direction add stiffeners
Beam Deflection & Design 11 Lecture 21
Architectural Structures I ENDS 231
S2008abn
Shear in Web
plate girders and stiffeners
Beam Deflection & Design 12 Lecture 21
Architectural Structures I ENDS 231
S2008abn
Beam Design
1. Know Fall for the material or FU for LRFD 2. Draw V & M, finding Mmax 3. Calculate Sreqd
h
( f b Fb )
b
4. Determine section size
Beam Deflection & Design 13 Lecture 21 Architectural Structures I ENDS 231
bh S= 6
2
S2008abn
Beam Design
4*. Include self weight for Mmax
and repeat 3 & 4 if necessary
5. Consider lateral stability
Unbraced roof trusses were blown down in 1999 at this project in Moscow, Idaho.
Photo: Ken Carper
Beam Deflection & Design 14 Lecture 21
Architectural Structures I ENDS 231
S2008abn
Beam Design
6. Evaluate shear stresses - horizontal
( f v F...
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