Explanation Calculation: Draw the asymmetrical I section as Figure (1). Refer Figure (1), Consider the section 1. Calculate the area of the section 1 ( A 1 ) : A 1 = ( 12 + 12 ) × 6 = 144 mm 2 Calculate the moment of inertia of the section 1 ( I 1 ) : I 1 = 24 × 6 3 12 = 432 mm 4 Calculate the centroid of the section 1 ( y 1 ) from neutral axis: y 1 = 24 + 6 2 = 27 mm Calculate the moment of inertia of the section 1 ( I x ) 1 about x axis using the formula: ( I x ) 1 = I 1 + A 1 y 1 2 Substitute 432 mm 4 for I 1 , 144 mm 2 for A 1 , and 27 mm for y 1 . ( I x ) 1 = 432 + ( 144 ) × 27 2 = 105408 mm 4 Consider the section 2. Calculate the area of the section 2 ( A 2 ) : A 2 = ( 24 + 24 ) × 8 = 384 mm 2 Calculate the moment of inertia of the section 2 ( I 2 ) : I 2 = 8 × 48 3 12 = 73728 mm 4 Calculate the centroid of the section 2 ( y 2 ) from neutral axis: Since the neutral axis is acting at the center, y 2 = 0 . Calculate the moment of inertia of the section 2 ( I x ) 2 about x axis using the formula: ( I x ) 2 = I 2 + A 2 y 2 2 Substitute 73728 mm 4 for I 2 , 384 mm 2 for A 2 and 0 mm for y 2 . ( I x ) 2 = 73728 + ( 384 ) × 0 2 = 73728 mm 4 Consider the section 3. Calculate the area of the section 3 ( A 3 ) using the formula: A 3 = ( 24 + 24 ) × 6 = 288 mm 2 Calculate the moment of inertia of the section 3 ( I 3 ) : I 3 = 48 × 6 3 12 = 864 mm 4 Calculate the centroid of the section 3 ( y 3 ) from neutral axis: y 3 = 24 + 6 2 = 27 mm Calculate the moment of inertia of the section 3 ( I x ) 3 about x axis: ( I x ) 3 = I 3 + A 3 y 3 2 Substitute 864 mm 4 for I 3 , 288 mm 2 for A 3 and 27 mm for y 3

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

Videos

Question

Chapter 9.2, Problem 9.31P

To determine

The moment of inertia (Ix) and radius of gyration (kx) of the shaded area with respect to the x axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.1, Problem 9.30P

Chapter 9.2, Problem 9.32P

Students have asked these similar questions

Trieed a detailed drawing Win explanatio LL Antsmi 1981x pu + 96252 اه 6. The Pre-combustion chamber design engines employ nozzle type commonly referred to as a ....... a. inward-opening nozzle b. multiple-hole nozzle. c. pintle nozzle. d. none of these. 7. If the temperature of the spark plug tip is less than 350 °C, ......... a. the plug might not work. b. the carbon deposits would increase. 8. Port injection sprays fuel....... c. pre-ignition will occur. d. none of these. a. towards the intake valve. b. in the engine cylinder. c. in the throttle body assembly. d. none of these. 9. When the fuel-air mixture changed from best power to a richer ratio, the spark advance should be........ a. increased. b. decreased. c. left unchanged. d. none of these. d. none of these. 10. Spark plugs are classified as hot plugs and cold plugs depending upon ........ a. spark gap. b. the type of plug c. the operating temperature insulator. range of the electrode tip. ---20125 750 x2.01 SP 5.

A 1. How does the octane number (O.N.) of the fuel a. Higher ignition advance is required for a high O.N. fuel. b. Higher ignition retard is required for a high O.N. fuel. affect spark ing:d. Nou does not affect spark timing. c. The octane number 2. How does the ignition system account for load change? these. of a. The throttle b. The vacuum ignition governor c. The mechanism of d. None of is wide opened. provide additional spark advance at part throttle positions. centrifugal advance does the job. these. 3. In the common rail fuel system the fuel is metered by ........ a. low pressure pump. b. injectors. c. high pressure pump. d. none of these. 4.......... is the time period, measured in degrees of cam rotation, during which the contact points remain closed between each opening. a. Distributor. b. Dwell. c. ECU. d. none of these. 5. The trigger wheel in TCI system replaces the ......... used in a contact breaker distributor. a. pickup coil. b. distributor cam. c. condenser. 750 x2.01…

a い يكا 4 +91- pu Answer the following statements by true or false, giving the reason for your answer: 1. Injection pressure in CI engines should be sufficiently high. 2. The purpose of the condenser in battery ignition system is to prevent spark in the ignition coil assembly. 3. An idling engine requires lean mixture of fuel and air. 4. Factors which decide optimum engine firing order are engine vibration, engine cooling and back pressure. 5. It is the duty of the header to control over speeding during CI engine operation when drastic reduction in load occurs. ---20125 750 x2.01 SP

Chapter 9 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - Prob. 9.3P Ch. 9.1 - Prob. 9.4P Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - Prob. 9.7P Ch. 9.1 - Prob. 9.8P Ch. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - Prob. 9.10P

Knowledge Booster

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.

The moment of inertia ( I x ) and radius of gyration ( k x ) of the shaded area with respect to the x axis.

Concept explainers

Videos

The moment of inertia (Ix) and radius of gyration (kx) of the shaded area with respect to the x axis.

Want to see the full answer?

Chapter 9 Solutions