Structural Engineering - UMassK12

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University of Massachusetts Amherst

Structural Engineering

Sergio F. Breña


STEM Education Institute

Saturday Workshop

September 30, 2006


University of Massachusetts Amherst

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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