BuyFind*arrow_forward*

6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 47P

Textbook Problem

221 views

Using the conjugate-beam method, determine the smallest moments of inertia *I* required for the beams shown in Figs. P6.18 through P6.22, so that the maximum beam deflection does not exceed the limit of 1/360 of the span length (i.e., Δ_{max} ≤ *L*/ 360).

FIG. P6.21, P6.47

To determine

Find the smallest moment of inertia (*I*) required for the beam if the deflection does not exceed the limit

Given information:

The Young’s modulus is 30 GPa.

**Calculation:**

Consider the flexural rigidity *EI* of the beam is constant.

Show the free body diagram of the given beam as in Figure (1).

Refer Figure (1),

Consider upward forces are positive and downward forces are negative.

Consider clockwise moments are negative and counterclockwise moments are positive.

Determine the support reaction at *A* using the Equation of equilibrium;

Determine the reaction at support C;

Show the reactions of the given beam as in Figure (2).

Refer Figure (2),

Determine the bending moment at support *A*;

Determine the bending moment at *B*;

Determine the bending moment at *C*;

Determine the bending moment at *D*;

Show the

Show the conjugate-beam as in Figure (4).

Take moment about point *D*:

Determine the support reaction at *A* of a conjugate

The maximum deflection will occur for the given beam at point *M* and take a distance of *B*.

Determine the intensity of load at

Determine the shear force at *M* using the relation;

Here, *b* is the width and h is the height of respective triangle and rectangle.

Substitute

Structural Analysis

Show all chapter solutions

Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - Determine the equations for slope and deflection...Ch. 6 - Determine the equations for slope and deflection...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - 6.7 and 6.8 Determine the slope and deflection at...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point B of...

Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point A of...Ch. 6 - Use the moment-area method to determine the slopes...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - 6.18 through 6.22 Determine the smallest moment of...Ch. 6 - 6.18 through 6.22 Determine the smallest moment of...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - Determine the maximum deflection for the beam...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.31 and 6.32 Use the moment-area method to...Ch. 6 - Use the moment-area method to determine the slope...Ch. 6 - Use the moment-area method to determine the slopes...Ch. 6 - 6.33 and 6.34 Use the moment-area method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.39 Determine the slope and deflection at point A...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - Using the conjugate-beam method, determine the...Ch. 6 - Using the conjugate-beam method, determine the...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - Determine the maximum deflection for the beams...Ch. 6 - Determine the maximum deflection for the beams...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.57 and 6.58 Use the conjugate-beam method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.59 and 6.60 Use the conjugate-beam method to...Ch. 6 - 6.59 and 6.60 Use the conjugate-beam method to...

Find more solutions based on key concepts

Show solutions The grain size distributions of four soils A, B, C, and D are shown in Figure 2.26. Without carrying out any co...

Fundamentals of Geotechnical Engineering (MindTap Course List)

Use A992 steel and select a structural me for the top chord of the welded roof truss shown in Figure P3.8-l. Al...

Steel Design (Activate Learning with these NEW titles from Engineering!)

Repeat Example 8-6 assuming that the highest flow rate in each collection leg is 750 cubic feet per minute at 1...

Solid Waste Engineering

Repeat Problem 2.8 using the following data. 2.8 The following are the results of a sieve and hydrometer analys...

Principles of Geotechnical Engineering (MindTap Course List)

Is concrete better in supporting compressive loads or tensile loads?

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

Ensure that the only legal values for the BDRMS column in the CONDO_UNIT table are 1, 2, or 3.

A Guide to SQL

client (456) a. standard that outlines characteristics of how two devices communicate on a network b. guideline...

Enhanced Discovering Computers 2017 (Shelly Cashman Series) (MindTap Course List)

Give some examples of database connectivity options and what they are used for.

Database Systems: Design, Implementation, & Management

What is an alert roster? What is an alert message? Describe the two ways they can be used.

Management Of Information Security

List the eight main guidelines for user Interface design. How would you rank them in order of importance? Expla...

Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

A motor is tripping out on overload. The motor nameplate reveals a full-load current of 68 amperes. When the mo...

Electric Motor Control

The resultant of the two forces has a magnitude of 800 lb. Determine the direction of the resultant and the mag...

International Edition---engineering Mechanics: Statics, 4th Edition

Sales Discount Policies Consider three businesses, all of which offer price reductions to their customers. The ...

Cornerstones of Financial Accounting

The high-side pressure on a system with a cycling clutch and pressure cycling switch is 245 psi, the low- side ...

Automotive Technology: A Systems Approach (MindTap Course List)

Which security protocols are used to protect e-mail?

Principles of Information Security (MindTap Course List)

While discussing the power flow through a five-speed transmission while it is in first gear: Technician A says ...

Automotive Technology

2 What are the advantages of ERP systems over standalone software packages?

Fundamentals of Information Systems

Why is it important to minimize cable clutter in a rack?

Network+ Guide to Networks (MindTap Course List)

An object has a mass of 10 lbm. A. Find the change in potential energy when it is lifted from the ground to 25 ...

Fundamentals of Chemical Engineering Thermodynamics (MindTap Course List)

How does materials requirement planning support the purchasing process in an ERP environment? What are some of ...

Principles of Information Systems (MindTap Course List)

Write the X- and Z-axis coordinates for the part show n. Use the diametral method in the X-axis.

Precision Machining Technology (MindTap Course List)

Briefly explain how HDFS and MapReduce are complementary to each other.

Database Systems: Design, Implementation, & Management

Software is valuable in helping individuals, workgroups, and entire enterprises achieve their goals. Applicatio...

Fundamentals of Information Systems

A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). Separate segments are jo...

Mechanics of Materials (MindTap Course List)

Describe in simple terms the three types of standby power systems. ______

EBK ELECTRICAL WIRING RESIDENTIAL

If your motherboard supports ECC DDR3 memory, can you substitute non-ECC DDR3 memory?

A+ Guide to Hardware (Standalone Book) (MindTap Course List)

Why is the torch tip raised as the cutting lever is depressed when cutting a hole?

Welding: Principles and Applications (MindTap Course List)