Basic structural theory. Statics Things dont continue to move if forces are resisted – Static...
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Transcript of Basic structural theory. Statics Things dont continue to move if forces are resisted – Static...
![Page 1: Basic structural theory. Statics Things dont continue to move if forces are resisted – Static Equilibrium What resists the force? Equal and opposite Reaction.](https://reader036.fdocuments.net/reader036/viewer/2022062511/55182cf65503469d318b4e99/html5/thumbnails/1.jpg)
Basic structural theory
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Statics
Things don’t continue to move if forces are resisted – Static
Equilibrium
What resists the force? Equal and opposite Reaction
Things deflect if forces are resisted
Elastic and Plastic Deformation
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Basic loads (forces)
Vertical (y only)
Lateral (x only)
Rotational (moment)
Concentrated loads
Distributed loadsw = P/l
force-couple
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Basic components
Linear – Column, Beam
Planar – Wall, Floor
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Basic connections
Simple (constrain y in direction of gravity, rotate freely)
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Basic connections
Roller (constrain y, rotate freely)
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Basic connections
Pin (constrain x & y, rotate freely)
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Basic connections
Pin (constrain x & y, rotate freely)
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Basic connections
Cable (Pin with tension only)
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Basic connections
Cable (Pin with tension only)
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Basic connections
Fixed/Rigid (constrain x, y, rotation)
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Basic connections
Fixed/Rigid (constrain x, y, rotation)
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Basic connections
Fixed/Rigid (constrain x, y, rotation)
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Basic connections
Fixed/Rigid (constrain x, y, rotation)
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Basic connections
Misleading pin connections
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Column – Vertical Load
Axial load – Compression & Tension
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Column – Lateral Load
Non-axial (lateral) load – Buckling in compression
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Beam – Vertical Load
Non-axial load – Deflection
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Basic loads (forces)
Reactions are the same for Concentrated loads and Distributed
loads
Beam stresses are different
w = P/l
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Greater deflection
Greater max. moment
w = P/l
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CN
T
Beam – Stresses
Compression, Tension, Neutral axis
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Beam – Concentrated Vertical Load
Resist bending with Moment connection
Greater deflection
Greater max. moment
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Beam – Distributed Vertical Load
Resist bending with Moment connection
Greater deflection
Greater max. moment
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Factors influencing deflection:
P = load
l = length between supports
E = elastic modulus of material (elasticity)
I = Moment of inertia (depth/weight of beam)
Dmax = Pl 3/48EI
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Elastic modulus of materials
Structural Steel = 200 GPa (29,023,300 lb/in2)
Titanium = 110 GPa (15,962,850 lb/in2)
Aluminum = 70 GPa (10,158,177 lb/in2)
Concrete = 21 GPa (3,047,453 lb/in2)
Douglas Fir = 13 GPa (1,886,518 lb/in2)
Why are titanium and aluminum used in aircraft?
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Yield Strength of materials
Structural Steel=350-450 MPa
Titanium (Alloy)=900-1400 MPa
Aluminum=100-350 MPa
Concrete=70 MPa (compressive)
Douglas Fir= N/A
Density of materials
Structural Steel = 489 lb/ft3
Titanium = 282 lb/ft3
Aluminum = 169 lb/ft3
Concrete = 150 lb/ft3
Douglas Fir = 32 lb/ft3
1 lb/in2 = 6891 Pa
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Moment of Inertia of beam
Dependent on cross-sectional geometry
Not dependent on material properties
Icc = Moment of inertia of a rectangle about the neutral axis – i.e. it’s centroid = width x height3 /12
Ixx = Moment of inertia of a rectangle about an axis parallel to the neutral axis = Icc + width x height x (distance between axes)2
Centroid = S (Area x distance to bending axis)/(Total area)
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Triangulated frame (Truss) – increase depth of beam
Triangulated – all members axially loaded (truss) – no moments
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Triangulated frame (Truss) – increase depth of beam
Triangulated – all members axially loaded (truss) – no moments
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Rigid Frame – Vertical load
Reduce deflection: Rigid connection
Columns resist force and deflect
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Rigid Frame – Vertical load
Thrust develops at base of columns and must be resisted
(beam / foundation / grade beam)
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Cantilever
Moment connection
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Cantilever
Moment connection
tension
compression
moment (force-couple)
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Cantilevered Beam – Vertical load
Greater deflection
Greater max. moment
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Simple Frame – Vertical load
Reduce deflection at mid-span: Cantilever
Lesser deflection
Lesser max. moment
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Cantilever
Deflection - Resist bending with counterweight
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Frame – Lateral load
Racking
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Frame – Lateral load
Racking
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Frame – Lateral load
Triangulated – all members axially loaded (truss) – no moment
connections
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Frame – Lateral load
Triangulated – all members axially loaded (truss) – no moment
connections
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Frame – Lateral load
Rigid (moment-resisting) frame
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Frame – Lateral load
Rigid (moment-resisting) frame
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Frame – Lateral load
Shear-resisting (force in plane)
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Frame – Lateral load
Pre-engineered shear panel
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Frame – Lateral load
Pre-engineered shear panel
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Frame – Lateral load
Shear-resisting (force in plane)
Non-structural partitions
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Frame – Lateral load
Shear-resisting (force in plane)
Masonry must be grouted and steel-reinforced
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Funicular structures
Tension (Cable)
Compression (Arch)
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Funicular structures
Tension (Cable)
Compression (Arch)
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Funicular structures
Tension (Cable)
Compression (Arch)
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Non-Funicular structures
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Materials - Wood
Tension & compression, no rigid connection
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Materials - Wood
Unpredictable failure mode (non-uniform material – organic)
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Materials - Reinforced Concrete
Wide range of possible forms
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Materials - Reinforced Concrete
Compression and some tension (steel), rigid connection through rebar
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Materials - Reinforced Concrete
Catastrophic failure mode
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Materials - Reinforced Concrete
Catastrophic failure mode
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Materials - Reinforced Concrete
Lab testing
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Materials - Steel
Tension & compression
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Materials - Steel
Rigid connection through welding
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Materials - Steel
Plastic failure mode