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1
four
design methods
& beams
Methods & Beams Lecture 4 1 Applied Architectural Structures
lecture
Forum, Pompeii
APPLIED ARCHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS
Methods & Beams 2 Architectural Structures III
Allowable Stress Design
- historical method
- a.k.a. working stress, stress design
- stresses stay in ELASTIC range
Allowable Stress Design
- codes
- wood
- National Design Specification
- Manual of Timber Construction (glulam)
- masonry
- Masonry Specification Joint Code
- steel
- Steel Joist Institute
- American Institute of Steel Construction
Methods & Beams Lecture 4 3 Architectural Structures III
www.thfrc.gov
Limit State Design
- stresses go to limit (strain outside elastic range)
- loads may be factored
- resistance or capacity reduced by a factor
- based on material behavior
- “state of the art”
Methods & Beams Lecture 4 4 Architectural Structures III
www.thfrc.gov
2
Limit State Design
- codes
- wood
- National Design Specification
- masonry
- Masonry Specification Joint Code
- concrete
- American Concrete Institute
- Precast & Prestressed Concrete
- steel
- American Institute of Steel Construction Methods & Beams Lecture 4 5 Architectural Structures III
Reinforced Concrete Design
- ultimate strength design
- factor applied to capacity
- different for flexure, shear, bearing....
- factors applied to loads (ASCE 7)
- may be different for combinations
- can use alternate values & factors (older codes) Methods & Beams Lecture 4 6 Architectural Structures III
𝑈 = 1. 2 𝐷 + 1. 6 𝐿 𝑈 = 1. 2 𝐷 + 1. 0 𝑊 + 1. 0 𝐿 ⋮
Reinforced Concrete Design
- want steel to yield first
- ductile failure
- underreinforced
- find flexure capacity or resistance from
- ultimate stresses in steel
- “uniform stress block” in concrete
Methods & Beams Lecture 4 7 Architectural Structures III
4
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p
M
M
k
y
p
f
M
Z
S
k Z
5
Methods & Beams 17Lecture 3
Beams
- maximum stress distribution
- principal stresses
- resultant of shear and bending stress
Methods & Beams 18Lecture 3abn
Beams
EI
M(x) curvature dx
d y 2
2
U.Washington – ENGR 220
Methods & Beams 19Lecture 3
Beams
- design:
- bending stress not exceeding allowable or limit stress
I
Mc
Fall fb
all
req' d
F
M
S
Methods & Beams 20Lecture 3
Beams
- bending stresses dominate
- shear stresses exist horizontally with shear
- no shear stresses with pure bending
7
Beam Design
- Consider lateral stability (cont)
- lateral buckling caused by compressive forces at top couples with insufficient rigidity
- can occur at low stress levels
- stiffen or brace
Aweb
V
A
V
max
I
VQ
q
Ib
VQ
ave
Beam Design
- Provide adequate bearing area at supports
- Evaluate torsion
J
T ρ
T
T
T L
A
P
f p
8
Methods & Beams 29Lecture 3
Beam Design
- Torsion (cont)
2
c 1 ab
T
τmax
J
T ρ
4 2
J ^1 πc
Methods & Beams 30Lecture 3 A
Beam Design
- Torsion (cont)
1 3 ab
T
τmax
Methods & Beams 31Lecture 3 abn
Beam Design
- Evaluate deflections
Methods & Beams 32Lecture 3
Deflection Limits
- based on service condition, severity
L/
L/
L/
L/
L/
DL+LL
Roof or floor (damageable elements)
Ordinary Usage L/
Floor beams:
no plaster L/
plaster ceiling L/
Commercial
Industrial L/
Roof beams:
Use LL only
10
Beam Materials
- timber
- glu-lam wood
- concrete
- steel
- reinforced masonry
Methods & Beams Lecture 3 38 Architectural Structures III
Tools – Multiframe
- in computer lab (Multiframe3D w/ text)
Methods & Beams Lecture 3 39 Architectural Structures III
Tools – Multiframe
- frame window
- define beam members
- select points, assign supports
- select members, assign section
- load window
- select point or member, add point or distributed loads
Methods & Beams Lecture 3 40 Architectural Structures III ARCH 631 F2007abn
Tools – Multiframe
- to run analysis choose
- plot
- choose options
- double click (all)
- results
