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Structures 213 b
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Gravity
Key Concepts:
Terms in this set (51)
Shear walls
are least flexible but good for apartments and hotels with party walls
Cantilevers
provide the least intrusion at ground floor
Moment frames
are most flexible, good for office buildings
Braced frames
are more flexible than walls but less flexible than moment frames bracing is usual around central cores
Concrete moment resistant joint
rebars extend through beam and column
Steel moment resistant joint:
beam flanges welded to column flanges; stiffener plates between column flanges resist bending stress of beam flanges
Beam depth and weight
increase with span
• very long beam fails under its own weight
Economic limit
is reached before most capacity is required to support self-weight
Short spans cost less than long spans
Just like beams, other structures have capacity limits
• Capacity limits include minimum spans; for example:
• Cost of joints makes short span trusses expensive
• Cost of fittings makes short span cables expensive
Span / depth ratios
Structure elements and systems have optimal L/d (span / depth) ratios that may be defined as
10 - 20 - 30 rule:
L/d = 10 for trusses and suspension cables
• L/d = 20 for beams
• L/d = 30 for slabs and decks
Span Range:
Recommended min. and max. spans
Span/Depth ratio:
For simple supports, use average ratio
Adjust Depth:
• Decrease @ light load and close spacing
• Increase @ heavy load and wide spacing
• Decease @ elements with overhangs
• Double @ cantilevers
Horizontal Elements
Rupture length
is the length a material can hang before breaking under its own weight (compression for concrete and masonry)
Roof live load
is 20 psf in areas without snow,
like Los Angeles, but up to 400 psf in mountains
Light-weight structures
Light-weight structures are effective in areas of earthquakes, like California, since seismic forces are mass times acceleration (f = m a)
• Ductile steel and wood structures
• Ductile steel and wood structures are effective to absorb dynamic seismic load
Stiff concrete shear walls
are effective to resist wind load but they increase seismic load
Heavy structures
are effective in areas of strong wind load, like Florida
Thermal loads
are critical in areas of great temperature variation, like Chicago
Stiffness
is defined by the moment of inertia I:
Strength
is defined by Section modulus S = I/c:
glue
The same amount of material is 100 times stiffer and 10 times stronger when glued to resist shear to engage fibers in tension and compression.
Beams
resist bending by a couple, with 2/3 beam depth d as lever arm; compression C on top and tension T on bottom.
Truss
resist the global moment by a couple, with truss depth d as lever arm; compression C in top and tension T in bottom chord. Max. moment yields max. chord forces.
C = T =M / d
Suspension cables
resist the global moment by a couple, with sag f as lever arm. The resisting couple consists of horizontal reaction H and horizontal cable force at mid-pan; with max. cable force at supports, where H, vertical reaction R and cable tension T form an equilibrium vector triangle:
T = (H2 + R2)1/2
Arch
resist global moments by a couple like cables, but in compression instead of tension:
C = (H2+R2)1/2
Radial pressure
Radial pressure per unit length acting on a circular ring yields ring tension
T=Rp
Single point load
Triangle
Uniform load
Parabola
Self weight
Catenary
Sag/span vs. force
small sag = large force
• Large sag = small force
• Large sag requires costly tall support
• Optimal span/sag is usually 10
Glu Lam
Glu Lam Roof Beams
Chord Forces/ Allowable Concentric Loads
Space Truss
span 2-ways. Thus are only effective for equal spans both ways.
At unequal spans:
The longer span would only carry a fraction of the load.
Truss Details
Cable Stayed Structures
Vierendeel Steel Girder
-do they resist gravity load by axial, bending, tension, or compression stress?
Axial
-where is bending stress maximum/minimum?
Ends
-where is shear stress maximum/minimum?
Middle
Hyperbolic Paraboloid (HP) shells
Vierendeel girder and frame
Exhibit Hall Hanover
Trusses Overview
-Truss-which bars are in tension and compression?
Verts are compressions, Horizontal is tension, |\|/| (Pratt) diagonals are tension, |/|\| (Howe) diagonals are compression
-where do the maximum forces occur?
Maximum bending in middle, maximum shear on ends
-if given truss spacing and uniform load, know how to calculate tributary truss joist load
W=w x e
-are space trusses good for one-way or two-way spanning?
2 way
-where is bending stress maximum/minimum?
Max in middle
-where is shear stress maximum/minimum?
Max on ends
-Pratt truss = v Howe truss = ^
-10-20-30 Rule (L/D)
10- trusses/cable, 20- beams/girder, 30- slabs/deck
Arches
-Arch-do they resist load in tension, compression, or bending? -sag/span vs. force (Lect 7, pg 3)
Compression
-Cable-under uniform load, does a cable assume a catenary or parabolic shape?
Parabolic
-under self-weight, does a cable assume a catenary or parabolic shape?
Catenary
-do they carry load in tension, compression, or bending?
Compression
Suspension Structure
Suspension Structures
-do suspension roofs resist wind uplift though dead weight, cable compression, or surface curvature?
Surface curvature
-are suspension roofs good for short, medium, or long spans?
Long
-sag/span vs. force (Lect 7, pg 3)
-The Golden Gate Bridge is a _ structure?
Suspension
Wood
-what is the best advantage of using wood (according to Prof Schierle)?
Only renewable material
-what is typical spacing for joists?
16in
-what is the typical plywood sheet size?
4'x8'
-what is the maximum span of a gluelam beam?
200 ft
-what is the individual board size that comprises a gluelam beam?
1/2in
-should members span in the long or short direction?
Short
-in a simply supported beam, where is bending stress maximum/minimum?
Middle
-in a simply supported beam, where is shear stress maximum/minimum?
Ends
-what do hold downs do?
Shear walls to foundation
-what do anchor bolts do?
Beams to walls
Steel
-what is steel's modulus of elasticity (E)?
29 ksi
-is steel ductile, brittle, or flexible?
Ductile
Fabric Structures
-what is the difference between synclastic and anticlastic structures?
Anticlastic is 2 way (saddle shape). Synclastic is 1 way (Dome shape).
-what is the difference between air supported and air inflated structures?
Air Inflated is an inflatable tube that acts as structure. Air supports is the entire support come from air (parachute).
-do anticlastic roofs resist gravity, wind uplift, or both?
both
Folded Plate vs Cylindrical Shell
Prismatic Structures
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