Page 606.Consider the Figure 9.10 (a) of Concept Problem 9.2,which is asimply supported prismatic beam with a uniformly distributed load w per unit length.A. First, solve the Concept Problem 9.2 problem as statedB. Now let’s add an upward point load P located on third of the length from point A. The point load is applied as point D. Solve the problemC. With the results of b, what is was a function of P in order to have zero displacement at point D? What are the slopes at Points A, D and BD,Can you think of a different structure that would have the same deflection profile as in c, with the appropriate boundary conditions. Explain in detail but concisely. WOXR₁=TwL(b)(a)D[x = 0, y=0](c)[x=Ly=0](d)Fig. 9.10 (a) Simply supportedbeam with a uniformly distributedload. (b) Free-body diagram ofsegment AD. (c) Boundary conditions.(d) Point of maximum deflection.Concept Application 9.2The simply supported prismatic beam AB carries a uniformly distributed loadw per unit length (Fig. 9.10a). Determine the equation of the elastic curve andthe maximum deflection of the beam.Draw the free-body diagram of the portion AD of the beam (Fig. 9.10b)and take moments about D forM = {wLx - wx²(1)Substituting for M into Eq. (9.4) and multiplying both members of thisequation by the constant El givesIntegrating twice in .x,EIordyEI ==dxdxEl y = -1== wx² +y =1=-=-=wXx²* + = 2 ²x² + C₁x + C₂24- 7/7wx² + = w²x³² + C₁10=w+w+G₁LC₁=-wL²Carrying the values of C, and C₂ back into Eq. (9.4), the elastic curve isEl y=-wx+wLx-wLxwLxObserving that y = 0 at both ends of the beam (Fig. 9.10c), let x = 0and y = 0 in Eq. (4) and obtain C₂ = 0. Then make x = L and y = 0 in thesame equation, soW24EI(-x+ 2Lx¹ - L³x)Wc == 24 E 7 (-16 + 21-²2 - 1²¹²) =2LL8lylmax =SwL384EISubstituting the value for C, into Eq. (3), we check that the slope of thebeam is zero for x = L/2 and thus that the elastic curve has a minimum atthe midpoint C (Fig. 9.10d). Letting x = L/2 in Eq. (5),The maximum deflection (the maximum absolute value) is(2)5wL384EI(3)(5)

NOTE : Since you have posted a question with multiple sub-parts, we will solve the first three…

Answered: Page 606.Consider the Figure 9.10 (a)…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

Page 606.Consider the Figure 9.10 (a) of Concept Problem 9.2,which is asimply supported prismatic beam with a uniformly distributed load w per unit length.

A. First, solve the Concept Problem 9.2 problem as stated

B. Now let’s add an upward point load P located on third of the length from point A. The point load is applied as point D. Solve the problem

C. With the results of b, what is was a function of P in order to have zero displacement at point D? What are the slopes at Points A, D and B

D,Can you think of a different structure that would have the same deflection profile as in c, with the appropriate boundary conditions. Explain in detail but concisely.

WOX
R₁=TwL
(b)
(a)
D
[x = 0, y=0]
(c)
[x=Ly=0]
(d)
Fig. 9.10 (a) Simply supported
beam with a uniformly distributed
load. (b) Free-body diagram of
segment AD. (c) Boundary conditions.
(d) Point of maximum deflection.
Concept Application 9.2
The simply supported prismatic beam AB carries a uniformly distributed load
w per unit length (Fig. 9.10a). Determine the equation of the elastic curve and
the maximum deflection of the beam.
Draw the free-body diagram of the portion AD of the beam (Fig. 9.10b)
and take moments about D for
M = {wLx - wx²
(1)
Substituting for M into Eq. (9.4) and multiplying both members of this
equation by the constant El gives
Integrating twice in .x,
EI
or
dy
EI ==
dx
dx
El y = -
1
== wx² +
y =
1
=-=-=wXx²* + = 2 ²x² + C₁x + C₂
24
- 7/7wx² + = w²x³² + C₁
1
0=w+w+G₁L
C₁=-wL²
Carrying the values of C, and C₂ back into Eq. (9.4), the elastic curve is
El y=-wx+wLx-wLx
wLx
Observing that y = 0 at both ends of the beam (Fig. 9.10c), let x = 0
and y = 0 in Eq. (4) and obtain C₂ = 0. Then make x = L and y = 0 in the
same equation, so
W
24EI
(-x+ 2Lx¹ - L³x)
W
c =
= 24 E 7 (-16 + 21-²2 - 1²¹²) =
2L
L
8
lylmax =
SwL
384EI
Substituting the value for C, into Eq. (3), we check that the slope of the
beam is zero for x = L/2 and thus that the elastic curve has a minimum at
the midpoint C (Fig. 9.10d). Letting x = L/2 in Eq. (5),
The maximum deflection (the maximum absolute value) is
(2)
5wL
384EI
(3)
(5)

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 9 steps with 16 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions