8 6 Sin Cos Ratios Noted
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This document provides a review of using trigonometric ratios (sine, cosine, tangent) to solve for unknown sides or angles of right triangles. It gives examples of using trig ratios to find missing sides or angles, including the sine ratio to solve for an opposite side when given the hypotenuse and adjacent side, and the cosine ratio to solve for the adjacent side when given the hypotenuse and opposite side. The key takeaway is that memorizing the mnemonic SOHCAHTOA (Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent) can help keep the trigonometric ratios organized when solving right
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1) USING ELASTIC DESIGN , SELECT AN
ADEQUATE WIDE FLANGE FOR ALL THE
HIGHLIGHTED (IN RED) MEMBERS. WRITE
YOUR SELECTION RIGHT OVER THE MEMBER
(LIKE ON THE BEAMS ALONG GRID 1)
-USE ASD OR LRFD, YOUR CHOICE.
REMEMBER THAT LRFD IS LESS
CONSERVATIVE.
-SEE NOTES FROM THE PROJECT MANAGER
IN THE NEXT PAGE.
-SHOW YOUR CALCS FOR EVERY BEAM.
-EXTRA CREDITS (HW_pointsx1.2):
DESIGN THE ENTIRE FRAMING PLAN.
Assignment 05
Structural Steel Design NAME & STUDENT ID
Remember that after you make sure that your beam is safe, you should check that your
deflections stays below L/360 under live load and below L/240 under total load, at minimum.
NOTE: Do not factor the loads when you compute deflection.
NOTES FROM PROJECT MANAGER:
GENERAL NOTE:
WE HAVE HEIGHT RESTRICTIONS ON THE FLOOR BELOW, PLEASE KEEP THE BEAMS DEPTH AS SHALLOW
AS POSSIBLE AND STRICTLY UNDER 16.1 INCHES . ALSO MIND AT BUDGET AND ALWAYS TRY TO
CHOSE THE MOST ECONOMICAL SHAPE.
NOTE A:
PLEASE LIMIT THE SIZE OF THIS BEAM TO W10, W12 MAX; ALSO, WE ARE ATTACHING A FANCY FACADE
TO THIS BEAM, THE MANUFACTURER TOLD ME THAT THIS BEAM CANNOT DEFLECT MORE THAN 1/2"
OR THE FACADE WILL CRACK.
NOTE B:
PLEASE MIND THAT I AM TRYING TO HIDE THIS BEAM
IN THE PARTITION WALL (7 1/2" THICK). SEE SKETCH
Assignment 05
Structural Steel Design NAME & STUDENT ID
SEE NOTE A
SEE NOTE B
PARTITION WALL
7.5"
Assignment 05
Structural Steel Design NAME & STUDENT ID
- Use this page to write your calculations (you can print this page multiple times)
- No messy calcs. Don't forget dimensions.
Assignment 05
Structural Steel Design NAME & STUDENT ID
2) Look at note A, without the height restriction, what would be the most efficient shape to use in this
case? Write a note to your project manager, explaining why you had to select a heavy wide flange,
explain what stiffness is, and the role of the moment of inertia in this selection (your project manager
did not take a steel design class).
3) Look at note B, use both ASD and LRFD to select this shape. Do you feel LRFD helps you better
meeting all the restrictions? Why?
4) In your own words, describe the behavior of the cross section below when subjected to a point load
as shown. Make sure to indicate tension and compression, explain the stress distribution and don't
forget to mention the role of the moment of inertia. Feel free to get aided by formulas, sketches and
diagrams.
Cross section
P
L1 L2
APPENDIX 44.A
Elastic Beam Deflection Equations
(w is the load per unit length.)
(y is positive downward.)
Case 1: Cantilever with End Load Case 2: Cantilever with Uniform Load
¨C
¨C
L
x
V
Mmax
yx
P reactions:
Rl ? 0
Rr ? P
shear:
V ? ?P ?constant?
moments:
Mx ? ?Px
Mmax ? ?PL
end slope:
?l ? ? PL
2
2EI
?r ? 0
deflection:
yx ? P
6EI
? ?
? ?2L3 ? 3L2x ? x3?
ymax ? PL
3
3EI
at x ? 0
¨C
¨C
L
x
Vr
Mr
yx
w reactions:
Rl ? 0
Rr ? wL
shear:
V x ? ?wx
V max ? ?wL ? V r
moments:
Mx ? ? wx
2
2
Mmax ? ? wL
2
2
? Mr
end slope:
?l ? ? wL
3
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This math worksheet contains 3 problems: 1) Find the value of x if y is 5, 7, or 10 with no other information given; 2) Solve the equation 2x - 4 = y + 3 for x, where y could be any value; 3) Solve for r in an equation with no other details provided.Solve Eq Notes 01
Solve Eq Notes 01Mr. Hohman
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The document provides instructions for students to learn how to solve basic addition and subtraction equations. It includes 5 examples of equations for students to practice solving, such as r + 16 = -7 and 8 = m - 3. The steps demonstrated include drawing a line to separate the equation, then adding or subtracting values from both sides to isolate the variable. The goal is for students to be able to solve one-step equations using these fundamental arithmetic operations.
Literal Eq Notes
Literal Eq NotesMr. Hohman
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Solving literal equations involves finding the value of a variable in terms of other variables or constants. Examples of solutions to literal equations include x = 3y - a, y = 4 + x/r, and solving equations such as 3x - 4y = 7, dx - 2y = 3z, y = mx + b, or by + 2 = c/3 for the variable on one side of the equal sign.Translate And Fraction Example 01
Translate And Fraction Example 01Mr. Hohman
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The document contains 3 math word problems to translate into equations: 1) x - 18 = 12, which can be written as x = 30. 2) 85 - 5x = 10, which can be written as 5x = 75 so x = 15. 3) 4x + 15 = 83, which can be written as 4x = 68 so x = 17.
Solve Eq Notes 02
Solve Eq Notes 02Mr. Hohman
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This document discusses how to solve equations using addition and subtraction properties of equality. It explains that to solve an equation means to isolate the variable on one side. It then introduces the addition property of equality, which states that if a = b, then a + c = b + c, meaning any number can be added to both sides of an equation without changing whether it is true. Several examples are worked through to demonstrate adding and subtracting various numbers from both sides of an equation. Finally, the subtraction property of equality is presented similarly.Solve Eq Example 01
Solve Eq Example 01Mr. Hohman
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This math problem involves solving two equations for the variable x. The first equation is x - 3 = 5, which can be solved to get x = 8. The second equation is 2(x - 4) = 2, which can be solved to get x = 6. Since x cannot equal both 8 and 6, the system of equations has no solution.Chapter 3 Quiz 1 Review
Chapter 3 Quiz 1 ReviewMr. Hohman
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The document summarizes key concepts in geometry including alternate interior angles, same side interior angles, corresponding angles, parallel lines, and perpendicular lines. It asks questions about which angles are equal, supplementary, or perpendicular when given information about parallel or perpendicular lines. It also asks how many lines can be drawn through a point that are parallel or perpendicular to a given line.Review Chapter 2
Review Chapter 2Mr. Hohman
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This cumulative review covers chapters 1 and 2, with 17 multiple choice questions testing the reader's understanding of the key events, characters, and ideas discussed in those chapters. The questions cover a range of details and ask the reader to think critically about cause-and-effect relationships, character motivations and themes in the chapters.1 5 Postulates And Theorems Relating Points, Lines Filled In
1 5 Postulates And Theorems Relating Points, Lines Filled InMr. Hohman
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The document outlines several postulates and theorems relating points, lines, and planes in geometry:
Postulate 5 states that a line contains at least two points, a plane contains at least three non-collinear points, and space contains at least four points not all in one plane.
Postulate 6 states that through any two points there is exactly one line. Postulate 7 states that through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane.
Theorems 1-1 and 1-3 state that if two lines intersect, they intersect at exactly one point and there is exactly one plane containing the lines. Theorem 1-2Chapter 4 Quiz 1 Review
Chapter 4 Quiz 1 ReviewMr. Hohman
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This document discusses whether different geometric figures are congruent. It asks if four pairs of figures are congruent without providing the figures, indicating the document is assessing a student's ability to determine congruency based on the definition of congruency.3 1 Parallel Lines And Planes Filled Out
3 1 Parallel Lines And Planes Filled OutMr. Hohman
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Parallel lines and planes are coplanar and do not intersect. Skew lines are noncoplanar and do not intersect. If two parallel planes are cut by a third plane, the lines of intersection will be parallel. A transversal is a line that intersects two or more coplanar lines. Alternate interior angles and same side interior angles are pairs of angles related to a transversal. Corresponding angles are in corresponding positions relative to two lines.2-5
2-5Mr. Hohman
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Two lines are perpendicular if they intersect at a right angle. If two lines form a right angle, or congruent adjacent angles, then the lines are perpendicular. If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.13 3 And 13 4
13 3 And 13 4Mr. Hohman
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The document is notes from a math class covering topics like coordinate planes, circles, parallel and perpendicular lines, vectors, and SPICSA. It includes definitions, formulas, and examples for these concepts. Sections 1 through 7 provide explanations and review of geometric shapes, slopes of lines, vectors, and how to add and multiply vectors. Section 8 indicates there will be practice problems from the covered materials.12 2 and 12 3
12 2 and 12 3Mr. Hohman
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This document reviews the formulas for calculating the lateral area, surface area, and volume of prisms, pyramids, cylinders, and cones. It notes that the formulas for cylinders are identical to those for prisms, and the formulas for cones are identical to those for pyramids. Some example problems are included for prisms and pyramids. The document concludes by listing page numbers from the textbook for additional even-numbered practice problems.12 1 Prisms Filled Out
12 1 Prisms Filled OutMr. Hohman
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The document defines and provides information about prisms. It states that a prism is a 3D solid with two congruent bases that are parallel planes. It also defines lateral faces and edges. The document provides formulas for calculating the lateral area and total surface area of right prisms. It gives an example of calculating the volume of a right trapezoidal prism and using the volume formula of a cube to solve an algebra problem.Recently uploaded (20)
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8 6 Sin Cos Ratios Noted
- 1. 8-6 The Sine and Cosine Ratios
- 2. Review Tangent X Z Y opp adj hyp
- 3. Tangent example X Z Y a 14 34 ?
- 4. What about the hypotenuse? X Z Y a 14 34 ? c
- 5. Sine X Z Y opp adj hyp
- 6. sin 24 ¡ã= ? 0.4023 0.9135 0.4067 0.4463 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
- 7. sin ___ = 0.4856 26 ¡ã 29 ¡ã 45 ¡ã 0.0085 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
- 8. Solve for x. 2.3 2.0 3.3 2.8 X 9 23 ¡ã 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
- 9. Cosine X Z Y opp adj hyp
- 10. cos 24 ¡ã= ? 0.4023 0.6754 0.9135 0.4463 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
- 11. Solve for x. 17 5 13 14 X 12 23 ¡ã 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
- 12. How are we going to keep this all together?
- 13. ?
- 14. SOHCAHTOA
- 15. SPICSA Page 314 2-16 even