Architectural Structures: Understanding Forces, Moments, and Physics in Design, Slides of Structural Design and Architecture

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ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

three

forces and

moments

Forces & Moments 1Lecture 3

lecture

Systems & Planning 2Lecture 3 Architectural Structures

Structural Math

• quantify environmental loads
  • how big is it?
• evaluate geometry and angles
  • where is it?
  • what is the scale?
  • what is the size in a particular direction?
• quantify what happens in the structure
  • how big are the internal forces?
  • how big should the beam be?

Forces & Moments 4 Lecture 3 Architectural Structures

Physics for Structures

• measures
  • US customary & SI

Units US SI Length in, ft, mi mm, cm, m Volume gallon liter Mass lb mass g, kg Force lb force N, kN Temperature F C

Forces & Moments 5Lecture 3

Physics for Structures

• scalars – any quantity
• vectors - quantities with direction
  • like displacements
  • summation results in the “straight line path” from start to end
  • normal vector is perpendicular to something

y

x

z

Forces & Moments 8Lecture 3

Geometry

• angles
  • right = 90º
  • acute < 90º
  • obtuse > 90º
  •  = 180º
• triangles
  • area
  • hypotenuse
  • total of angles = 180º

2

b  h 

A B^2  A C^2  B C^2

A

B

C

Forces & Moments 9Lecture 3

Geometry

• lines and relation to angles
  • parallel lines can’t intersect
  • perpendicular lines cross at 90º
  • intersection of two lines is a point
  • opposite angles are equal when two lines cross   



Forces & Moments 11Lecture 3

Geometry

• sides of two angles are parallel and intersect opposite way, the angles are supplementary - the sum is 180 °
• two angles that sum to 90 ° are said to be complimentary

 

 



Forces & Moments 12Lecture 3

• sides of two angles bisect a right angle (90 ° ), the angles are complimentary
• right angle bisects a straight line, remaining angles are complimentary

Geometry







    9 0



Architectural Structures

Trigonometry

• for right triangles

C^ 

B

A

CB

AB hypotenuse

opposite side sin   sin  

CB

AC hypotenuse

adjacent side cos   cos 

AC

AB adjacent side

opposite side tan   tan 

SOHCAHTOA

Forces & Moments 14 Lecture 3

Architectural Structures

Trigonometry

• for all triangles
  • sides A, B & C are opposite angles ,  & 
  • LAW of SINES
  • LAW of COSINES

A B C

sin  sin  sin   

A^2  B^2  C^2  2 B C c o s

A

 C B 



Forces & Moments 17Lecture 3

Architectural Structures

Algebra

• solving one equation
  • only works with one variable
  • ex:
    • add to both sides
    • divide both sides
    • get x by itself on a side

2 x  1  0 2 x  1  1  0  1

x ^12

2

1 2

2  

 x

2 x  1

Forces & Moments 19Lecture 3

Architectural Structures

Algebra

• solving one equations
  • only works with one variable
  • ex:
    • subtract from both sides
    • subtract from both sides
    • divide both sides
    • get x by itself on a side

2 x  1  4 x  5

2 x  1  2 x  4 x  5  2 x

 1  5  2 x  5  5

2

2 2

3 2 2

6 

  

   

 x

x   3 Forces & Moments 20 Lecture 3

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

Forces & Moments 22 Lecture 3 Architectural Structures

Force

• “action of one body on another that

affects the state of motion or rest of the body”

• Newton’s 3 rd^ law:
  • for every force of action there is an equal and opposite reaction along the same line

Forces & Moments 23Lecture 3 Architectural Structures

http://www.physics.umd.edu