Geometry angles right = 90 acute < 90 obtuse > 90 = - - PowerPoint PPT Presentation

S2019abn Introduction 63 Lecture 1 Elements of Architectural Structures ARCH 614

Geometry

• angles

– right = 90º – acute < 90º – obtuse > 90º –  = 180º

• triangles

– area – hypotenuse – total of angles = 180º

2 h b 

2 2 2

BC AC AB  

A B C

S2019abn Introduction 64 Lecture 1 Elements of Architectural Structures ARCH 614

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

   

S2019abn Introduction 65 Lecture 1 Elements of Architectural Structures ARCH 614

Geometry

– intersection of a line with parallel lines results in identical angles – two lines intersect in the same way, the angles are identical

          

S2019abn Introduction 68 Lecture 1 Elements of Architectural Structures ARCH 614

– similar triangles have proportional sides

Geometry

B C E A A B C A C B

DE BC AE AC AD AB   C B BC C A AC B A AB        

D      

S2019abn Introduction 69 Lecture 1 Elements of Architectural Structures ARCH 614

Trigonometry

• for right triangles

C



B A

CB AB hypotenuse side

• pposite

    sin sin CB AC hypotenuse side adjacent     cos cos AC AB side adjacent side

• pposite

    tan tan

SOHCAHTOA

S2019abn Introduction 72 Lecture 1 Elements of Architectural Structures ARCH 614

Trigonometry

• for all triangles

– sides A, B & C are opposite angles ,  &  – LAW of SINES – LAW of COSINES

C B A    sin sin sin    cos 2

2 2 2

BC C B A   

A



C B

 

S2019abn Introduction 74 Lecture 1 Elements of Architectural Structures ARCH 614

Algebra

• solving one equation

– only works with one variable – ex:

• add to both sides
• divide both sides
• get x by itself on a side

1 2   x 1 1 1 2     x

2 1

 x 2 1 2 2    x 1 2  x

S2019abn Introduction 75 Lecture 1 Elements of Architectural Structures ARCH 614

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

5 4 1 2    x x x x x x 2 5 4 2 1 2      5 5 2 5 1      x 2 2 2 2 3 2 6          x

3   x

S2019abn Introduction 76 Lecture 1 Elements of Architectural Structures ARCH 614

Algebra

• solving two equation

– only works with two variables – ex:

• look for term similarity
• can we add or subtract to eliminate one term?
• add
• get x by itself on a side

8 3 2   y x 6 3 12   y x 6 8 3 12 3 2      y x y x

14 14  x

1 14 14 14 14    x x

S2019abn Introduction 78 Lecture 1 Elements of Architectural Structures ARCH 614

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