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

Geometry • angles – right = 90º – acute < 90º – obtuse > 90º –  = 180º • triangles B b  h  – area 2 A C – hypotenuse   2 2 2 AB AC BC – total of angles = 180º Introduction 63 Elements of Architectural Structures S2019abn Lecture 1 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   Introduction 64 Elements of Architectural Structures S2019abn Lecture 1 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    Introduction 65 Elements of Architectural Structures S2019abn Lecture 1 ARCH 614

Geometry – similar triangles have proportional sides A AB AC BC   AD AE DE C B E A  D  A  C  AB AC BC          A B A C B C    C B B  Introduction 68 Elements of Architectural Structures S2019abn Lecture 1 ARCH 614

Trigonometry • for right triangles B opposite side AB     sin sin  hypotenuse CB C A adjacent side AC     cos cos hypotenuse CB opposite side AB     tan tan adjacent side AC SOHCAHTOA Introduction 69 Elements of Architectural Structures S2019abn Lecture 1 ARCH 614

Trigonometry • for all triangles  C – sides A, B & C are opposite B angles  ,  &    A – LAW of SINES    sin sin sin   A B C – LAW of COSINES     2 2 2 A B C 2 BC cos Introduction 72 Elements of Architectural Structures S2019abn Lecture 1 ARCH 614

Algebra • solving one equation – only works with one variable   – ex: 2 x 1 0     2 x 1 1 0 1 • add to both sides 2  x 1  x • divide both sides 2 1   2 2 • get x by itself on a side  x 1 2 Introduction 74 Elements of Architectural Structures S2019abn Lecture 1 ARCH 614

Algebra • solving one equations – only works with one variable    – ex: 2 x 1 4 x 5 • subtract from both sides      2 x 1 2 x 4 x 5 2 x • subtract from both sides      1 5 2 x 5 5      • divide both sides 6 3 2 2 x     2 2 2 • get x by itself on a side   3 x Introduction 75 Elements of Architectural Structures S2019abn Lecture 1 ARCH 614

Algebra • solving two equation – only works with two variables  y  – ex: 2 x 3 8  y  • look for term similarity 12 x 3 6 • can we add or subtract to eliminate one term?      2 x 3 y 12 x 3 y 8 6 • add 14  14 x 14 x 14 • get x by itself on a side    x 1 14 14 Introduction 76 Elements of Architectural Structures S2019abn Lecture 1 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 Introduction 78 Elements of Architectural Structures S2019abn Lecture 1 ARCH 614