Chapter 5

Deflection and Deflection and StiffnessStiffness

A. Aziz Bazoune

04/20/23 Chapter 5 1

OutlineOutline1. Spring Rates2. Deflection in Tension, Compression & Torsion3. Deflection due to Bending4. Strain Energy5. Castigliano’s Theorem 6. Statically Indeterminate Problems 7. Compression Members

Long Columns with Central LoadingIntermediate Length Columns with Central Loading

04/20/23 Chapter 5 2

Solved Solved ProblemsProblems

Lec. 14Lec. 14Lec. 14Lec. 14

04/20/23 Chapter 5 3

04/20/23 Chapter 5 4

04/20/23 Chapter 5 5

04/20/23 Chapter 5 6

04/20/23 Chapter 5 7

04/20/23 Chapter 5 8

ProblemProblem

SolutionSolutionSolutionSolution

1/2 1/22 2 6

31

2 2 1 30 10101.9

57 10y

l CE

k S

l

k

04/20/23 Chapter 5 9

ProblemProblem

l k

4 2

2

64 4

4.5 12172.8

4 1.25 / 416

ft inin

l ll k

I A d d

l l

dd

1l k l k

2 2 6

2 2

30 109906

( / ) (172.8

1

)

crP EC

A L k

2 21.259906 9906 9906 12150

4 4lbcr

DP A

04/20/23 Chapter 5 10

ProblemProblem

SolutionSolutionSolutionSolution

1 12xx

xx

bIk

A

3h

b

185.196

12 12mm

h

h

04/20/23 Chapter 5 11

ProblemProblem

1 12yyyy

I hk

A

3bb h

123.464

12 12mm

b

yy xxk k / / 280 / 3.464 80.83yyl k l k

1/2 1/22 2 9

61

2 2 1.2 207 10/ 130

290 10y

CEl k

S

1/ / J ohnson's Columnl k l k

04/20/23 Chapter 5 12

04/20/23 Chapter 5 13

ProblemProblem

2

266 6

9

1

2

290 10 1290 10 80.8 234 10

2 21 07 1.2 02N/ m

cr yy

SP LS

k ECA

6 6 6234 10 234 10 18 12 10 50,544NcrP A

04/20/23 Chapter 5 14

ProblemProblem

SolutionSolutionSolutionSolution

23 3A w t t t t

3t A

04/20/23 Chapter 5 15

ProblemProblem

SolutionSolutionSolutionSolution

23 3A w t t t t

3t A

3 3 4 41 12 1 12 3 4 0.25xxI bh t t t t

3 3 4 41 12 1 12 3 27 12 2.25yyI hb t t t t

04/20/23 Chapter 5 16

ProblemProblem

04/20/23 Chapter 5 17

Leonhard Euler

Portrait by Johann Georg Brucker

BornApril 15, 1707(1707-04-15)Basel, Switzerland

Died

September 18 [O.S. September 7] 1783St Petersburg, Russia

ResidencePrussiaRussiaSwitzerland

Nationality Swiss

Field Mathematics and physics

Institutions

Imperial Russian Academy of Sciences

Berlin AcademyAlma mater

University of Basel

Religion Calvinist[1]

Leonhard Paul Euler (pronounced Oiler; IPA [ˈɔʏlɐ]) (April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swiss mathematician and physicist, who spent most of his life in Russia and Germany. He published more papers than any other mathematician of his time.[2]

Euler made important discoveries in fields as diverse as calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[3] He is also renowned for his work in mechanics, optics, and astronomy.Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest of all time. He is also one of the most prolific; his collected works fill 60–80 quarto volumes.[4] A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the teacher (master) of us all".[5]

Euler was featured on the sixth series of the Swiss 10-franc banknote[6] and on numerous Swiss, German, and Russian postage stamps. The asteroid 2002 Euler was named in his honor. He is also commemorated by the Lutheran Church on their Calendar of Saints on May 24.

http://en.wikipedia.org/wiki/Leonhard_Euler

04/20/23 Chapter 5 18

QUESTIONQUESTIONS ?S ?