EBK MECHANICS OF MATERIALS
EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220100257063
Author: BEER
Publisher: YUZU
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 9.2, Problem 11P

For the beam and loading shown, (a) express the magnitude and location of the maximum deflection in terms of w0, L, E, and I. (b) Calculate the value of the maximum deflection, assuming that beam AB is a W18 × 50 rolled shape and that w0= 4.5 kips/ft, L = 18 ft, and E = 29 ×106 psi.

Chapter 9.2, Problem 11P, For the beam and loading shown, (a) express the magnitude and location of the maximum deflection in

Fig. P9.11

(a)

Expert Solution
Check Mark
To determine

The magnitude and location of the maximum deflection in terms of w0, L, E, and I.

Answer to Problem 11P

The location of the maximum deflection xm is 0.481L_.

The magnitude and location of the maximum deflection in terms of w0, L, E, and I is 0.00652w0L4EI_.

Explanation of Solution

Given that:

The length (L) of the beam is 18ft.

The load w0 is 4.5kips/ft.

The young’s modulus E is 29×106psi.

Calculation:

Sketch the free body diagram of beam as shown in Figure 1.

EBK MECHANICS OF MATERIALS, Chapter 9.2, Problem 11P , additional homework tip  1

Find the reactions of the beam.

RA+RB=12×wo×L

Take the moment at B.

RA×L(12×wo×L)(23×L)=0RA×LwoL23=0RA=woL23×1L=woL3

Find the reaction at B.

RA+RB=12×wo×LwoL3+RB=12×wo×LRB=woL2woL3=woL6

Take the section 1-1 at x distance from A as shown in Figure 2.

EBK MECHANICS OF MATERIALS, Chapter 9.2, Problem 11P , additional homework tip  2

Consider a section xx at a distance x from a.

Sketch the section x-x as shown in Figure 3.

EBK MECHANICS OF MATERIALS, Chapter 9.2, Problem 11P , additional homework tip  3

Calculate the intensity of loading w at the section x using similar triangle method as shown below:

wLx=w0Lw=w0L(Lx)

Find the shear force using the expression as follows:

dVdx=w=wo(Lx)L

Find the shear force using integration:

dVdx=wo(Lx)LV=woL(Lxx22)+CV=dMdx

Find the moment using the relation as follows:

dMdx=woL(Lxx22)+CVM=woL(Lx22x36)+CVx+CM (1)

Apply the boundary conditions:

When x=0, the moment M=0, substitute in Equation (1):

M=woL(Lx22x36)+CVx+CM0=woL(00)+0+CMCM=0

When x=L, the moment M=0.

Substitute 0 for CM and boundary condition in Equation (1):

M=woL(Lx22x36)+CVx+CM0=woL(L(L)22L36)+CVL+0=woL(L32L36)+CVL=woL(2L36)+CVL

CVL=woL(L33)CV=woL(L33)(1L)=woL3

Write the moment Equation:

EId2ydx2=M=woL(Lx22x36)+CVx+CM

Substitute woL3 for CV and 0 for CM.

EId2ydx2=woL(Lx22x36)+(w0L3)x+0=woL(Lx22x36)+(w0L3)x×(LL)=woL(Lx22x36L2x3)=woL(L2x3Lx22+x36) (2)

Integrate the Equation (2).

EId2ydx2=woL(L2x3Lx22+x36)EIdydx=woL(L2x26Lx36+x424)+C1 (3)

Integrate the Equation (3).

EIdydx=woL(L2x26Lx36+x424)+C1EIy=woL(L2x318Lx424+x5120)+C1x+C2 (4)

EIy=woL(L2x318Lx424+x5120)+C1x+C2

Apply the boundary condition in C2 as follows:

At x=0, y=0

Find the C2 value as shown follows:

Substitute 0 for x and 0 for y in Equation (4).

EIy=woL(L2(0)318L(0)424+(0)5120)+C1(0)+C2=woL(00+0)+0+C2C2=0

Apply the boundary condition in C1 as follows:

At x=L, y=0

Find the C1 value as shown follows:

Substitute 0 for x and 0 for y in Equation (4).

EI(0)=woL(L2(L)318L(L)424+(L)5120)+C1(L)+C20=woL(L518L524+(L)5120)+C1(L)+0C1(L)=woL(L545)C1(L)=woL445

C1=woL345

Substitute woL345 for C1 and 0 for C2 in Equation (4).

EIy=woL(L2x318Lx424+x5120)woL345x+0y=woEIL(118L2x3124Lx4+1120x5145L4x) (5)

Differentiate with respect to x in Equation (5).

dydx=woEIL(16L2x216Lx3+124x4145L4) (6)

To find the location of maximum deflection:

dydx=0

f=16L2xm216Lxm3+124xm4145L4

Consider the function z=xmL.

f(z)=16z216z3+124z4145 (7)

Differentiate with respect to z in Equation (7).

f(z)=16z216z3+124z4145dfdz=13zz22+16z3

Find the value z using Newton-Raphson method as follows:

z=z0f(z0)dfdz (8)

Show the calculated values of f(z), dfdz, and z values as shown in Table 1.

z0f(z)dfdzz
0.22-0.015830.0509080.53100
0.24-0.014790.0535040.51639
0.26-0.013690.0557960.50544
0.28-0.012560.0577920.49730
0.3-0.011380.05950.49134
0.32-0.010180.0609280.48708
0.34-0.008950.0620840.48415
0.36-0.00770.0629760.48224
0.38-0.006430.0636120.48111
0.4-0.005160.0640.48056
0.42-0.003870.0641480.48039
0.44-0.002590.0640640.48045
0.46-0.001310.0637560.48059
0.48-4.2E-050.0632320.4807
0.50000.00120.06250.4806
0.520.0024560.0615680.48010

Refer to table: 1.

The value of xm is 0.481L.

Find the value of ym using the relation as follows:

Substitute 0.481L for xm in Equation (5).

ym=woEIL(118L2(0.481L)3124L(0.481L)4+1120(0.481L)5145L4(0.481L))=woL4EIL(118(0.4807)3124(0.4807)4+1120(0.4807)5145(0.4807))=woL4EIL(0.006170.00222+0.000213880.01068)=0.00652woL4EIL

Therefore, he magnitude of the maximum deflection in terms of w0, L, E, and I is 0.00652w0L4EI_.

Therefore, the location of maximum deflection is 0.481L_.

(b)

Expert Solution
Check Mark
To determine

The value of maximum deflection.

Answer to Problem 11P

The value of maximum deflection is 0.229in._

Explanation of Solution

Calculation:

Convert kips/ft to lb/in.

w0=4.5kips/ft=450012=375lb/in.

The rolled shape section W18×50,

The value of I is 800in4.

Find the maximum deflection using the relation:

ym=0.00652w0L4EIL (9).

Substitute 375lb/in. for w0, 18ft for L, and 800in4 for I in Equation (9).

ym=0.00652375×18ft(12in1ft)29×106(800)=0.00652375×(216)429×106(800)=0.229in.

Thus, the value of maximum deflection is 0.229in._

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
36 2) Use the method of MEMBERS to determine the true magnitude and direction of the forces in members1 and 2 of the frame shown below in Fig 3.2. 300lbs/ft member-1 member-2 30° Fig 3.2. https://brightspace.cuny.edu/d21/le/content/433117/viewContent/29873977/View
Can you solve this for me?
5670 mm The apartment in the ground floor of three floors building in Fig. in Baghdad city. The details of walls, roof, windows and door are shown. The window is a double glazing and air space thickness is 1.3cm Poorly Fitted-with Storm Sash with wood strip and storm window of 0.6 cm glass thickness. The thickness of door is 2.5 cm. The door is Poor Installation. There are two peoples in each room. The height of room is 280 cm. assume the indoor design conditions are 25°C DBT and 50 RH, and moisture content of 8 gw/kga. The moisture content of outdoor is 10.5 gw/kga. Calculate heat gain for living room : الشقة في الطابق الأرضي من مبنى ثلاثة طوابق في مدينة بغداد يظهر في مخطط الشقة تفاصيل الجدران والسقف والنوافذ والباب. النافذة عبارة عن زجاج مزدوج وسمك الفراغ الهوائي 1.3 سم ضعيف الاحكام مع ساتر حماية مع إطار خشبي والنافذة بسماكة زجاج 0.6 سم سماكة الباب 2.5 سم. الباب هو تركيب ضعيف هناك شخصان في كل غرفة. ارتفاع الغرفة 280 سم. افترض أن ظروف التصميم الداخلي هي DBT25 و R50 ، ومحتوى الرطوبة 8…

Chapter 9 Solutions

EBK MECHANICS OF MATERIALS

Ch. 9.2 - For the beam and loading shown, (a) express the...Ch. 9.2 - (a) Determine the location and magnitude of the...Ch. 9.2 - For the beam and loading shown, determine the...Ch. 9.2 - Knowing that beam AE is a W360 101 rolled shape...Ch. 9.2 - For the beam and loading shown, knowing that a = 2...Ch. 9.2 - Knowing that beam AE is an S200 27.4 rolled shape...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - For the beam shown, determine the reaction at the...Ch. 9.2 - For the beam shown, determine the reaction at the...Ch. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - Prob. 27PCh. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - 9.29 and 9.30 Determine the reaction at the roller...Ch. 9.2 - 9.29 and 9.30 Determine the reaction at the roller...Ch. 9.2 - 9.37 and 9.32 Determine the reaction at the roller...Ch. 9.2 - 9.31 and 9.32 Determine the reaction at the roller...Ch. 9.2 - Prob. 33PCh. 9.2 - 9.33 and 9.34 determine the reaction at A and draw...Ch. 9.3 - 9.35 and 9.36 For the beam and loading shown,...Ch. 9.3 - 9.35 and 9.36 For the beam and loading shown,...Ch. 9.3 - 9.37 and 9.38 For the beam and loading shown,...Ch. 9.3 - 9.37 and 9.38 For the beam and loading shown,...Ch. 9.3 - 9.39 and 9.40 For the beam and loading shown,...Ch. 9.3 - 9.39 and 9.40 For the beam and loading shown,...Ch. 9.3 - 9.41 and 9.42 For the beam and loading shown,...Ch. 9.3 - 9.41 and 9.42 For the beam and loading shown (a)...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the timber beam and loading shown, determine...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - 9.51 and 9.52 For the beam and loading shown,...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam shown, and knowing that P = 40 kN,...Ch. 9.3 - 9.55 and 9.56 For the beam and loading shown, (a)...Ch. 9.3 - 9.55 and 9.56 For the beam and loading shown, (a)...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - Prob. 59PCh. 9.3 - 9.59 through 9.62 For the beam and loading...Ch. 9.3 - Prob. 61PCh. 9.3 - 9.59 through 9.62 For the beam and loading...Ch. 9.3 - The rigid bars BF and DH are welded to the...Ch. 9.3 - The rigid bar DEF is welded at point D to the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Prob. 84PCh. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - Prob. 96PCh. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - 9.99 and 9.100 For the uniform cantilever beam and...Ch. 9.5 - 9.99 and 9.100 For the uniform cantilever beam and...Ch. 9.5 - For the cantilever beam and loading shown,...Ch. 9.5 - Prob. 102PCh. 9.5 - Prob. 103PCh. 9.5 - Prob. 104PCh. 9.5 - Prob. 105PCh. 9.5 - For the cantilever beam and loading shown,...Ch. 9.5 - Two cover plates are welded to the rolled-steel...Ch. 9.5 - Two cover plates are welded to the rolled-steel...Ch. 9.5 - 9.109 through 9.114 For the prismatic beam and...Ch. 9.5 - Prob. 110PCh. 9.5 - Prob. 111PCh. 9.5 - Prob. 112PCh. 9.5 - Prob. 113PCh. 9.5 - Prob. 114PCh. 9.5 - Prob. 115PCh. 9.5 - 9.115 and 9.116 For the beam and loading shown,...Ch. 9.5 - Prob. 117PCh. 9.5 - 9.118 and 9.119 For the beam and loading shown,...Ch. 9.5 - Prob. 119PCh. 9.5 - Prob. 120PCh. 9.5 - Prob. 121PCh. 9.5 - Prob. 122PCh. 9.5 - Prob. 123PCh. 9.5 - Prob. 124PCh. 9.6 - 9.125 through 9.128 For the prismatic beam and...Ch. 9.6 - Prob. 126PCh. 9.6 - Prob. 127PCh. 9.6 - Prob. 128PCh. 9.6 - 9.129 and 9.130 For the beam and loading shown,...Ch. 9.6 - Prob. 130PCh. 9.6 - For the timber beam and loading shown, determine...Ch. 9.6 - Prob. 132PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 134PCh. 9.6 - Prob. 135PCh. 9.6 - Knowing that the beam AD is made of a solid steel...Ch. 9.6 - Prob. 137PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 139PCh. 9.6 - For the beam and loading shown, determine the...Ch. 9.6 - Prob. 141PCh. 9.6 - Prob. 142PCh. 9.6 - Prob. 143PCh. 9.6 - Prob. 144PCh. 9.6 - Prob. 145PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 147PCh. 9.6 - Prob. 148PCh. 9.6 - Prob. 149PCh. 9.6 - Prob. 150PCh. 9.6 - 9.151 and 9.152 For the beam and loading shown,...Ch. 9.6 - Prob. 152PCh. 9.6 - Prob. 153PCh. 9.6 - Prob. 154PCh. 9.6 - Prob. 155PCh. 9.6 - Fig. P9.155 and P9.156 9.156 For the beam and...Ch. 9 - For the loading shown, determine (a) the equation...Ch. 9 - Prob. 158RPCh. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Determine the reaction at A and draw the bending...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Beam CE rests on beam AB as shown. Knowing that a...Ch. 9 - The cantilever beam BC is attached to the steel...Ch. 9 - For the cantilever beam and loading shown,...Ch. 9 - Knowing that P = 4 kips, determine (a) the slope...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Determine the reaction at the roller support and...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Solids: Lesson 53 - Slope and Deflection of Beams Intro; Author: Jeff Hanson;https://www.youtube.com/watch?v=I7lTq68JRmY;License: Standard YouTube License, CC-BY