Problem

Coulomb's Law states that the force of attraction…

02:55

Problem 59 Easy Difficulty

The figure shows a beam of length $ L $ embedded in concrete walls. If a constant load $ W $ is distributed evenly along its length, the beam takes the shape of the deflection curve
$$ y = -\dfrac{W}{24EI} x^4 + \dfrac{WL}{12EI} x^3 - \dfrac{WL^2}{24EI} x^2 $$
where $ E $ and $ I $ are positive constants. ($ E $ is Young's modulus of elasticity and $ I $ is the moment of inertia of a cross-section of the beam.) Sketch the graph of the deflection curve.

Answer

see solution

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 5

Summary of Curve Sketching

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Samuel H.

University of Nottingham

Michael J.

Idaho State University

Watch More Solved Questions in Chapter 4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Video Transcript

So first, what we want to do is, um, sketch this curve so we see that we'll have why equals w divided by e i Times X to the fourth. And that can be a minus. And we also have minus 24 minus 24 ei times x to the fourth, actually plus w l divided by 12 ei times X to the third or X Cube. And then lastly, we'll have minus W l squared. Yeah, divided by 24 e I X squared. You know, creation. Using these properties, we can. Now I'm just select constants for our values, and we end up getting this graph. Now we can change these values. But what we ultimately see is that we'll have this somewhat parabolic shape that's always concave down S O. This is the general shape of our graph, Andi. That is the deflection curve that we can sketch based on the values and plotting points

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 5

Summary of Curve Sketching

Top Calculus 2 / BC Educators

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Samuel H.

University of Nottingham

Michael J.

Idaho State University