University of Massachusetts Amherst
Structural Engineering
Sergio F. Breña
STEM Education Institute
Saturday Workshop
September 30, 2006
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Outline
•
Introduction to Structural Engineering
•
Forces in Structures
•
Structural Systems
•
Civil Engineering Materials
•
Some Definitions of Important Structural
Properties
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Structural Engineering
•
What does a Structural Engineer do?
–
A Structural Engineer designs the structural
systems and structural elements in buildings,
bridges, stadiums, tunnels, and other civil
engineering works (bones)
–
Design: process of determining location, material,
and size of structural elements to resist forces
acting in a structure
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Engineering Design Process
•
Identify the problem (challenge)
•
Explore alternative solutions
–
Research past experience
–
Brainstorm
–
Preliminary design of most promising solutions
•
Analyze and design one or more viable solutions
•
Testing and evaluation of solution
–
Experimental testing (prototype) or field tests
–
Peer evaluation
•
Build solution using available resources (materials,
equipment, labor)
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Design Process in Structural Engineering
•
Select material for construction
•
Determine appropriate structural system for a
particular case
•
Determine forces acting on a structure
•
Calculate size of members and connections
to avoid failure (collapse) or excessive
deformation
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Examples of Typical Structures
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Forces in Structures
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Forces Acting in Structures
•
Forces induced by gravity
–
Dead Loads (permanent): self

weight of structure
and attachments
–
Live Loads (transient): moving loads (e.g.
occupants, vehicles)
•
Forces induced by wind
•
Forces induced by earthquakes
•
Forces induced by rain/snow
•
Fluid pressures
•
Others
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Forces Acting in Structures
Vertical: Gravity
Lateral: Wind, Earthquake
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Global Stability
Sliding
Overturning
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Forces in Structural Elements
100
lb
Compression
100
lb
Tension
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Forces in Structural Elements (cont.)
100
lb
Bending
Torsion
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Typical Structural Systems (1)
Arch
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Typical Structural Systems (2)
Truss
C
T
C
C
T
Forces in Truss Members
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Typical Structural Systems (3)
Frame
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Typical Structural Systems (4)
Flat Plate
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Typical Structural Systems (5)
Folded Plate
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Typical Structural Systems (6)
Shells
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Properties of Civil Engineering Materials
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Definition of Stress
Section X
T
T
Section X
Stress = Force/Area
T
Example (English Units):
T = 1,000 lb (1 kip)
A = 10 in
2
.
Stress = 1,000/10 = 100 lb/in
2
Example (SI Units):
1 lb = 4.448 N (Newton)
1 in = 25.4 mm
T = 1,000 lb x 4.448 N/lb = 4448 N
A = 10 in
2
x (25.4 mm)
2
= 6450 mm
2
(1 in)
2
Stress = 4448/6450 = 0.69 N/mm
2
(MPa)
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Definition of Strain
D
L
T
T
Lo
Strain =
D
L / Lo
Example:
Lo = 10 in.
D
L = 0.12 in.
Strain = 0.12 / 10 = 0.012 in./in.
Strain is dimensionless!!
(same in English or SI units)
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Stress
–
Strain Behavior of Elastic Mats.
Stress
Strain
E
E = Modulus of Elasticity = Stress / Strain
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Types of Stress

Strain Behavior
Stress
Strain
E
(a) Linear Elastic
Stress
Strain
(b) Non

linear Elastic
Stress
Strain
(c) Elastic

plastic
Stress
Strain
(d) Non

linear Plastic
Plastic strain
Plastic strain
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Materials Used in Civil Engineering
•
Stone and Masonry
•
Metals
–
Cast Iron
–
Steel
–
Aluminum
•
Concrete
•
Wood
•
Fiber

Reinforced Plastics
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Engineering Properties of Materials
•
Steel
–
Maximum stress: 40,000
–
120,000 lb/in
2
–
Maximum strain: 0.2
–
0.4
–
Modulus of elasticity: 29,000,000 lb/in
2
•
Concrete
–
Maximum stress: 4,000
–
12,000 lb/in
2
–
Maximum strain: 0.004
–
Modulus of elasticity: 3,600,000
–
6,200,000 lb/in
2
•
Wood
Values depend on wood grade. Below are some samples
–
Tension stress: 1300 lb/in
2
–
Compression stress: 1500 lb/in
2
–
Modulus of elasticity: 1,600,000 lb/in
2
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Concrete Components
•
Sand (Fine Aggregate)
•
Gravel (Coarse Aggregate)
•
Cement (Binder)
•
Water
•
Air
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Fiber

Reinforced Composites
Polymer
Matrix
Polyester
Epoxy
Vinylester
Fiber
Materials
Glass
Aramid (Kevlar)
Carbon
Function of fibers:
•
Provide stiffness
•
Tensile strength
Functions of matrix:
•
Force transfer to fibers
•
Compressive strength
•
Chemical protection
Composite
Laminate
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Important Structural Properties
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Engineering Properties of Structural Elements
•
Strength
–
Ability to withstand a given stress without failure
•
Depends on type of material and type of force (tension or
compression)
Tensile Failure
Compressive Failure
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Engineering Properties of Structural Elements
•
Stiffness (Rigidity)
–
Property related to deformation
–
Stiffer structural elements deform less under the same
applied load
–
Stiffness depends on type of material (E), structural shape,
and structural configuration
–
Two main types
•
Axial stiffness
•
Bending stiffness
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Axial Stiffness
D
L
T
T
Lo
Stiffness = T /
D
L
Example:
T = 100 lb
D
L = 0.12 in.
Stiffness = 100 lb / 0.12 in. = 833 lb/in.
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Bending Stiffness
Stiffness = Force / Displacement
Example:
Force = 1,000 lb
Displacement = 0.5 in.
Stiffness = 1,000 lb / 0.5 in. = 2,000 lb/in.
Displacement
Force
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Stiffness of Different Structural Shapes
Stiffest
Stiffer
Stiff
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Types of Structural Elements
–
Bars and
Cables
Bars can carry either tension
or compression
Cables can only carry tension
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Types of Structural Elements
–
Beams
Tension
Compression
Loads
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Providing Stability for Lateral Loads
Racking Failure of Pinned Frame
Braced Frame
Infilled Frame
Rigid Joints
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Concepts in Equilibrium
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Equilibrium of Forces (Statics)
•
Forces are a type of quantity called vectors
–
Defined by magnitude and direction
•
Statement of equilibrium
–
Net force at a point in a structure = zero
(summation of forces = zero)
•
Net force at a point is determined using a
force polygon to account for magnitude and
direction
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Moment (Rotational) Equilibrium
3 ft
6 ft
A
Moment of Force = Force x Distance
To neutralize rotation about point A,
moments from the two forces has to
be equal and opposite:
100 lb x 3 ft = 50 lb x 6 ft
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Force Calculation in Simple Structure
100
lb
8 ft
6 ft
A
C
B
36.9
Side BC
Side AB
=
8 ft
6 ft
=
1.333
Side AC
Side AB
=
10 ft
6 ft
=
1.667
Force
BC
=
1.333
Force
AB
Force
BC = 1.333 x 100 lb = 133.3 lb
Force
AC
=
1.667
Force
AB
Force
AC = 1.667 x 100 lb = 166.7 lb
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Graphic Statics
1 Square = 10 lb
100 lb
133.3 lb
36.9
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Force Transfer from Beams to Supports
Force, P
Span, L
1/3 L
2/3 L
2/3 P
1/3 P
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Force Transfer Example

Bridge
8,000 lb
32,000 lb
22,000 lb
*
18,000 lb
**
L = 60 ft
30 ft
30 ft
15 ft
45 ft
*Front axle: 8,000 lb x 45/60 = 6,000 lb
Rear axle: 32,000 lb x 30/60 = 16,000 lb
**Front axle: 8,000 lb x 15/60 = 2,000 lb
Rear axle: 32,000 lb x 30/60 = 16,000 lb
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