1 F2009abn six mechanics of materials Mechanics of Materials 1 Lecture 6 Architectural Structures ARCH 331 lecture www.carttalk.com ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN ARCH 331 DR. ANNE NICHOLS SPRING 2019 Mechanics of Materials 2 Lecture 5 Foundations Structures ARCH 331 F2008abn Mechanics of Materials • MECHANICS • MATERIALS Mechanics of Materials 3 Lecture 5 Foundations Structures ARCH 331 F2008abn Mechanics of Materials • external loads and their effect on deformable bodies • use it to answer question if structure meets requirements of – stability and equilibrium – strength and stiffness • other principle building requirements • economy, functionality and aesthetics Mechanics of Materials 4 Lecture 5 Foundations Structures ARCH 331 F2008abn Knowledge Required • material properties • member cross sections • ability of a material to resist breaking • structural elements that resist excessive – deflection – deformation
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1
F2009abn
six
mechanics
of materialsMechanics of Materials 1
Lecture 6
Architectural Structures
ARCH 331
lecture
www.carttalk.com
ARCHITECTURAL STRUCTURES:
FORM, BEHAVIOR, AND DESIGN
ARCH 331
DR. ANNE NICHOLS
SPRING 2019
Mechanics of Materials 2
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Mechanics of Materials
• MECHANICS • MATERIALS
Mechanics of Materials 3
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Mechanics of Materials
• external loads and their
effect on deformable bodies
• use it to answer question if structure
meets requirements of
– stability and equilibrium
– strength and stiffness
• other principle building requirements• economy, functionality and aesthetics
Mechanics of Materials 4
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Knowledge Required
• material properties
• member cross sections
• ability of a material to resist breaking
• structural elements that resist excessive
– deflection
– deformation
2
Mechanics of Materials 5
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Problem Solving
1. STATICS:
equilibrium of external forces,
internal forces, stresses
2. GEOMETRY:
cross section properties, deformations and
conditions of geometric fit, strains
3. MATERIAL PROPERTIES:
stress-strain relationship for each material
obtained from testing
Mechanics of Materials 6
Lecture 5
Foundations Structures
ARCH 331
F2008abn
A
Pfstress
Stress
• stress is a term for the intensity of a
force, like a pressure
• internal or applied
• force per unit area
Mechanics of Materials 7
Lecture 5
Foundations Structures
ARCH 331
F2008abn
• materials have a critical stress value
where they could break or yield
– ultimate stress
– yield stress
– compressive stress
– fatigue strength
– (creep & temperature)
Design
acceptance
vs. failure
Mechanics of Materials 8
Lecture 5
Foundations Structures
ARCH 331
F2008abn
allowableactual Ff • we’d like
• stress distribution may
vary: average
• uniform distribution
exists IF the member is
loaded axially
(concentric)
Design (cont)
3
Mechanics of Materials 9
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Scale Effect
• model scale
– material weights by volume,
small section areas
• structural scale
– much more material weight,
bigger section areas
• scale for strength is not
proportional:L
L
L
2
3
Mechanics of Materials 10
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Normal Stress (direct)
• normal stress is normal
to the cross section
– stressed area is
perpendicular to the
load
A
Pf cort
Mechanics of Materials 11
Lecture 5
Foundations Structures
ARCH 331
F2008abn
• stress parallel to a surface
Shear Stress
td
P
A
Pfv
ave
Mechanics of Materials 12
Lecture 5
Foundations Structures
ARCH 331
F2008abn
• stress on a surface by
contact in compression
Bearing Stress
td
P
A
Pf p
4
Mechanics of Materials 13
Lecture 5
Foundations Structures
ARCH 331
F2008abn
• normal stress caused by bending
Bending Stress
S
M
I
Mcfb
Mechanics of Materials 14
Lecture 5
Foundations Structures
ARCH 331
F2008abn
• shear stress caused by twisting
Torsional Stress
J
Tfv
Mechanics of Materials 15
Lecture 5
Foundations Structures
ARCH 331
F2008abn
• what structural elements see shear?
– beams
– bolts
– splices
– slabs
– footings
– walls
• wind
• seismic loads
Structures and Shear
connections
V
Mechanics of Materials 16
Lecture 5
Foundations Structures
ARCH 331
F2008abn
• connected members in tension cause
shear stress
• connected members in
compression cause
bearing stress
Bolts
5
Mechanics of Materials 17
Lecture 5
Foundations Structures
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F2008abn
• seen when 2 members are connected
Single Shear
4
2dv
P
A
Pf
Mechanics of Materials 18
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Double Shear
F=
• seen when 3 members are connected
• two areas
4d
v 2
2P
A
2P
A2
Pf
Mechanics of Materials 19
Lecture 5
Foundations Structures
ARCH 331
F2008abn
• compression & contact
• projected area
Bolt Bearing Stress
td
P
A
Pf
projected
p
F=
Mechanics of Materials 20
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Strain
• materials deform
• axially loaded materials change
length
• bending materials deflect
• STRAIN:
– change in length
over length + UNITLESS L
Lstrain
6
Mechanics of Materials 21
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Shearing Strain
• deformations
with shear
• parallelogram
• change in angles
• stress:
• strain:
– unitless (radians)
s
L
tanL
s
Mechanics of Materials 22
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Shearing Strain
• deformations
with torsion
• twist
• change in angle of line
• stress:
• strain:
– unitless (radians)
L
Mechanics of Materials 23
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Load and Deformation
• for stress, need P & A
• for strain, need & L
– how?
– TEST with load and
measure
– plot P/A vs.
Mechanics of Materials 24
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Material Behavior
• every material has its own response
– 10,000 psi
– L = 10 in
– Douglas Fir vs.
steel?
7
Mechanics of Materials 25
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Behavior Types
• ductile - “necking”
• true stress
• engineering stress
– (simplified)
A
Pf
oA
Pf
Mechanics of Materials 26
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Behavior Types
• brittle
• semi-brittle
Mechanics of Materials 27
Lecture 5
Foundations Structures
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Stress to Strain
• important to us in - diagrams:
– straight section
– LINEAR-ELASTIC
– recovers shape
(no permanent
deformation)
f
Mechanics of Materials 28
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Hooke’s Law
• straight line has constant slope
• Hooke’s Law
• E
– Modulus of elasticity
– Young’s modulus
– units just like stress
f
E
1
Ef
8
Mechanics of Materials 29
Lecture 5
Foundations Structures
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Stiffness
• ability to resist strain
• steels
– same E
– different
yield points
– different
ultimate strength
uf
Mechanics of Materials 30
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Isotropy & Anisotropy
• ISOTROPIC
– materials with E same at
any direction of loading
– ex. steel
• ANISOTROPIC
– materials with different E
at any direction of loading
– ex. wood is orthotropic
Mechanics of Materials 31
Lecture 5
Foundations Structures
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Elastic, Plastic, Fatigue
• elastic springs back
• plastic has permanent
deformation
• fatigue caused by
reversed loading
cycles
Mechanics of Materials 32
Lecture 5
Foundations Structures
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Plastic Behavior
• ductile
at yield stress
9
Mechanics of Materials 33
Lecture 5
Foundations Structures
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F2008abn
Lateral Strain
• or “what happens to the cross section
with axial stress”
• strain in lateral direction
– negative
– equal for isometric materials
E
f xx
0 zy ff
zy
Mechanics of Materials 34
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Poisson’s Ratio
• constant relationship between
longitudinal strain and lateral strain
• sign!
x
z
x
y
strainaxial
strainlateral
E
f xzy
5.00
Mechanics of Materials 35
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Calculating Strain
• from Hooke’s law
• substitute
• get
Ef
LE
A
P
AE
PL
Mechanics of Materials 36
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Orthotropic Materials
• non-isometric
• directional values of
E and
• ex:
– plywood
– laminates
– polymer
composites
10
Mechanics of Materials 37
Lecture 5
Foundations Structures
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F2008abn
• why we use f ave
• increase in stress atchanges in geometry
– sharp notches
– holes
– corners
–
Stress Concentrations
Mechanics of Materials 38
Lecture 5
Foundations Structures
ARCH 331
F2008abn
22
maxmax
f
A
Pf
o
v
• if we need to knowwhere max f and f v
happen:
Maximum Stresses
F
oA
Pf max1cos0
5.0sincos45
Mechanics of Materials 39
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Maximum Stresses
Mechanics of Materials 40
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Deformation Relationships
• physical movement
– axially (same or zero)
– rotations from axial changes
• relates to P
steel 20 kN
aluminum
AE
PL
11
Mechanics of Materials 41
Lecture 5
Foundations Structures
ARCH 331
F2008abn
Deformations from Temperature
• atomic chemistry reacts
to changes in energy
• solid materials• can contract with decrease in temperature