CHAPTER 1 Introduction to Statics

8/4/2019 CHAPTER 1 Introduction to Statics

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CHAPTER 1

INTRODUCTION TOSTATICS


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OBJECTIVES1. DESCRIBE THE FUNCTION AND USAGE OF STATICS

2. DEMONSTRATE KNOWLEDGE OF BASIC GEOMETRY

3. SOLVE FOR UNKNOWN ANGLES USING TRIGONOMETRY4. SOLVE FOR UNKNOWN ANGLES USING PYTHAGOREAN THEOREM

5. SOLVE FOR UNKNOWN ANGLES USING SIMILAR TRIANGLES THEOREM

6. DISTINGUISH SIGNIFICANT DIGITS IN A NUMBER

7. DEMONSTRATE ABILITY TO ROUND NUMBERS

8. DEMONSTRATE ABILITY TO PERFORM UNIT CONVERSIONS

9. CALCULATE FORCE AND WEIGHT


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the study of force, deformation and motion,

and the relations between them.


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STATICS the science of determining the forces and force systems acting on RIGID

bodies


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The Skywalk

Hualapai IndianReservation outside

of Las Vegas


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160 FT LONG, 72 FT HIGHSUSPENDED 90 FT IN THE AIR

WEIGHING IN AT 600 TONS(1,200,000 POUNDS)


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STATICS MATH ERROR

CHICAGO 2003

12 PEOPLE KILLED

30 PEOPLE SERIOUSLY HURTwww.youtube.com/watch?v=4OOg7vL3rNY&feature=related
http://www.youtube.com/watch?v=4OOg7vL3rNY&feature=relatedhttp://www.youtube.com/watch?v=4OOg7vL3rNY&feature=related


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I. ANGLES AND LINES

1. A straight line has 180 degrees on each side

2. If 2 lines (or more ) lines are parallel to the same line, they

are perpendicular to each other.

3. Intersecting lines create 2 pairs of opposite and equal

angles

4. Intersecting lines create a common vertex for 4 angles, the

sum of which is 360

g 1 =g 3

g 2 = g 4


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4. When 2 lines intersected by a third line:

- equal pairs of alternate interior angles are formed

- equal pairs of alternate exterior angles are formed

- equal pairs of interior and exterior corresponding angles are formed

< 3 = < 6

< 4 = < 5

< 1 = < 8

< 2 = < 7

< 1 = < 5< 2 = < 6

< 3 = < 7

< 4 = < 8

II. TRIANGLES

6. Right Triangle

-Contains one 90 degree angle

-the sum of remaining 2 angles = 90 degrees

5. Are three sided figures containing 3 angles that add up to 180 degrees.


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-contains two sides of equal length

-angles opposite the equal sides are also equal-the altitude divide the triangle into two congruent triangles

7. Isosceles Triangle

8. Equilateral Triangle

-Contains three equal sides

-The three angles are equal and measure 60 degrees


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9. Similar Triangles

Angle-Angle rule If 2 angles of 1 triangle are equal to 2 angles

of another triangle they are similar

6 = 9

2 S

350 350280 280

6 92 S

Side Angle Side rule If the angle of one triangle is the same as the angle of

Another triangle AND the sides containing these angles have the same ratio, the

Triangles are similar.

350

35

4 6

10

2S

5

4 = 6

2 S


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common applications

ALL OF THESE TRIANGLESARE SIMILAR!


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ONLY WORKS FOR RIGHT TRIANGLES


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3-4-5 TRIANGLES

52

=32

+42

Any triangle that has these

proportions must be a right triangle

by Pythagorean Theorem

6-8-109-12-15

12-16-20

15-20-25


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SIN

OPPOSITE

HYPOTENUSE COS

ADJACENT

HYPOTENUSE

TAN

OPPOSITE

ADJACENT


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OR


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LAW OF SINES

LAW OF COSINES


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sin corresponds to x axis

cos corresponds to y axis

If x is positive, cosine is positive.

If x is negative, cosine is negative.

If y is positive, sine is positive.If y is negative, sine is negative.

THEREFORE

Angle sin cos0o 0 1

90o 1 0

180o 0 -1

270o -1 0

OTHER USEFUL TRIG TRIVIA


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Systems of Linear Equations

y= 3x 2y= x 6STEP 1

Solve one equation to isolate one variable by itself, in this case the Y is already

done for us.y=3x-2

STEP 2

Substitute into the second equation, so that there will only be 1 type of

variable in it

3x 2 = x 6STEP 3

Solve for the unknownx = 1

STEP 4

Substitute that value back into the first equation to solve for the other

unknown variable y=3(1) 2 = 1


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OUTPUT CANNOT BE MORE ACCURATE THAN INPUT

58

7= 8.285714286

1)ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.

2)ALL zeroes between non-zero numbers are ALWAYS significant.

3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal

point AND at the end of the number are ALWAYS significant.

4) ALL zeroes which are to the left of a written decimal point and are in

a number >= 10 are ALWAYS significant.


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MATHEMATICS OF MEASUREMENT

ADDITION/SUBTRACTION

10ft + 5ft = 15ft

units are handled mathematically just like variables!

18in -10in =8 in

only like units may be added or subtracted

30 in + 5 ft - 3m


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MULTIPLICATION

TO MULTIPLY 3ft x 3ft = ?

multiply 3 x 3

multiply 1ft x 1ft

= 9 ft2

6in x 3in x 2in = 6 x 3 x 2

in x in x in = 36 in3

what about the like units rule?

1ft x 5 lb = 5 ft-lb


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DIVISION

10 ft 2 ft =

1. 10 2 = 5

2. ft ft = 1=ft

ft= 5

25 ft2 5 ft 1. 25 5 = 5

2. ft2 ft = ftft

ftft

ft

ft=

=

2

= 5ft

200 miles 3.5 hrs = 55 miles/hr

50 lb .25 in2 = 200 lb/in2

and, once again, unlike units?


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UNITY FRACTIONS

1 yd = 3 ft

ftyd3

1

yd

ft

1

3or

15 yd X

yd

ft

1

3

15 ft X

ft

yd

3

1


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2

2

2

2

37.1144

1

197 ftin

ft

in =

1 ft2 = 144 in2

1 ft3 = 1078 in3

1ft

1ft

=

12 in

12 in

1 ft(12 in)

1

ft(12

in)

1ft(12

in)


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UNITS OF FORCE

POUND (LB)KILOPOUND (KIP) = 1,000 LB

NEWTON (N)

KILONEWTON (Kn) = 1,000 N

FORCEAND WEIGHTARE USED INTERCHANGEABLY

F= ma

W = mg

F=force

m=mass

a=acceleration

W=weight

m=mass

g=acceleration due to gravity

(32.2 ft/sec2 or 9.81 m/sec2


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SI PREFIXES

1,000,000,000 bytes = 1,000,000 kilobytes = 1,000 megabytes = 1 gigabyte


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Documents

CHAPTER 1 Introduction to Statics