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S2018abn Forces 1 Lecture 2 Elements of Architectural Structures ARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

ARCH 614

• DR. ANNE NICHOLS

SPRING 2018

two

loads, forces and vectors

lecture

x y z

S2018abn Forces 2 Lecture 2 Elements of Architectural Structures ARCH 614

Structural Design

• planning
• preliminary structural

configuration

• determination of loads
• preliminary member

selection

• analysis
• evaluation
• design revision
• final design

S2018abn Forces 3 Lecture 2 Elements of Architectural Structures ARCH 614

• STATIC and DYNAMIC
• dead load

– static, fixed, includes building weight, fixed equipment

• live load

– transient and moving loads (including

• ccupants), snowfall

Structural Loads

S2018abn Forces 4 Lecture 2 Elements of Architectural Structures ARCH 614

• wind loads

– dynamic, wind pressures treated as lateral static loads on walls, up or down loads on roofs

Structural Loads

S2018abn Forces 5 Lecture 2 Elements of Architectural Structures ARCH 614

• earthquake loads

– seismic, movement of ground

Structural Loads

S2018abn Forces 6 Lecture 2 Elements of Architectural Structures ARCH 614

• impact loads

– rapid, energy loads

Structural Loads

S2018abn Forces 7 Lecture 2 Elements of Architectural Structures ARCH 614

Forces

• statics

– physics of forces and reactions on bodies and systems – equilibrium (bodies at rest)

• forces

– something that exerts on an object:

• motion
• tension
• compression

S2018abn Forces 8 Lecture 2 Elements of Architectural Structures ARCH 614

Forces

• “action of one body on another that

affects the state of motion or rest of the body”

• Newton’s 3rd law:

– for every force of action there is an equal and

• pposite reaction along

the same line

http://www.physics.umd.edu

S2018abn Forces 9 Lecture 2 Elements of Architectural Structures ARCH 614

Force Vectors

• applied at a point
• magnitude

– Imperial units: lb, k (kips) – SI units: N (newtons), kN

• direction
• sense

(tail) (tip)

S2018abn Forces 10 Lecture 2 Elements of Architectural Structures ARCH 614

• for statics, the bodies are ideally rigid
• can translate

and rotate

• internal forces are

– in bodies – between bodies (connections)

• external forces act on bodies

Forces on Rigid Bodies

translate rotate

S2018abn Forces 11 Lecture 2 Elements of Architectural Structures ARCH 614

• the force stays on the same line of

action

• truck can’t tell the difference
• only valid for EXTERNAL forces

Transmissibility

=

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Force System Types

• collinear

S2018abn Forces 13 Lecture 2 Elements of Architectural Structures ARCH 614

Force System Types

• coplanar

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Force System Types

• space

S2018abn Forces 15 Lecture 2 Elements of Architectural Structures ARCH 614

Adding Vectors

• graphically

– parallelogram law

• diagonal
• long for 3 or more vectors

– tip-to-tail

• more convenient

with lots of vectors

F P R F P R

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Force Components

• convenient to resolve into 2 vectors
• at right angles
• in a “nice” coordinate system
•  is between Fx and F from Fx

Fy Fx  F x y Fy Fx F Fy Fx F

 cos F Fx   sin F Fy 

2 2 y x

F F F  

x y

F F   tan

S2018abn Forces 17 Lecture 2 Elements of Architectural Structures ARCH 614

Trigonometry

• Fx is negative

– 90 to 270

• Fy is negative

– 180 to 360

• tan is positive

– quads I & III

• tan is negative

– quads II & IV

• 6
• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 6

• 6 -5 -4 -3 -2 -1 0

1 2 3 4 5 6

X Y

Quadrant I Quadrant II Quadrant III Quadrant IV

   

S2018abn Forces 18 Lecture 2 Elements of Architectural Structures ARCH 614

Component Addition

• find all x components
• find all y components
• find sum of x components, Rx (resultant)
• find sum of y components, Ry

2 2 y x

R R R  

x y

R R   tan

Fy Fx R Py Px  Rx Ry

S2018abn Forces 19 Lecture 2 Elements of Architectural Structures ARCH 614

Alternative Trig for Components

• doesn’t relate angle to axis direction
•  is “small” angle between F and

EITHER Fx or Fy

• no sign out of calculator!
• have to choose RIGHT

trig function, resulting direction (sign) and component axis

+/-? Fy +/-? Fx  F x y

S2018abn Forces 20 Lecture 2 Elements of Architectural Structures ARCH 614

Static Equilibrium

• balanced & steady
• no motion or translation
• equilibrant opposite resultant

X X

=

S2018abn Forces 21 Lecture 2 Elements of Architectural Structures ARCH 614

Cables

• simple
• uses

– suspension bridges – roof structures – transmission lines – guy wires, etc.

• have same tension all along
• can’t stand compression

http:// nisee.berkeley.ed/ugodden

S2018abn Forces 22 Lecture 2 Elements of Architectural Structures ARCH 614

Cables Structures

• use high-strength steel
• need

– towers – anchors

• don’t want movement

http:// nisee.berkeley.edu/godden

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Cable Loads

• straight line

between forces

• with one force

– concurrent – symmetric

S2018abn Forces 24 Lecture 2 Elements of Architectural Structures ARCH 614

Cable Loads

• shape directly

related to the distributed load

• funicular

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Cable Loads

• trig:
• parabolic (catenary)

– distributed uniform load

 cos T Tx 



2 2 /

) ( 4 L x Lx h y    sin T Ty 

h y x L

) L h L h ( L Ltotal

4 4 5 32 2 2 3 8

1   