Explanation Calculation: Sketch the cross section as shown in Figure 1. Find the moment of inertia ( I ¯ x ) 1 using the relation as shown below: ( I ¯ x ) 1 = 1 12 b 1 h 1 3 (1) Here, b 1 is width of the section 1 and h 1 is height of the section 1. Substitute 100 mm for b 1 and 8 mm for h 1 in Equation (1). ( I ¯ x ) 1 = 1 12 ( 100 ) × 8 3 = 4 , 266.67 mm 4 Find the moment of inertia ( I ¯ x ) 2 and ( I ¯ x ) 3 using the relation as shown below: ( I ¯ x ) 2 = ( I ¯ x ) 3 = 1 12 b 2 h 2 3 + ( b d ) y ¯ 2 (2) Here, b 2 is width of the section 2 and h 2 is height of the section 2. Substitute 8 mm for b 2 , 20 mm for y ¯ 2 , and 32 mm for h 2 in Equation (2). ( I ¯ x ) 2 = ( I ¯ x ) 3 = 1 12 ( 8 ) ( 32 ) 3 + ( 8 × 32 ) ( 20 ) 2 = 21 , 845.333 + 102 , 400 = 124 , 245.333 mm 4 Find the total moment of inertia ( I ¯ x ) using the relation as shown below: ( I ¯ x ) = ( I ¯ x ) 1 + ( I ¯ x ) 2 + ( I ¯ x ) 3 (3) Substitute 4 , 266.67 mm 4 for ( I ¯ x ) 1 , 124 , 245.333 mm 4 for ( I ¯ x ) 2 , and 124 , 245.333 mm 4 for ( I ¯ x ) 3 in Equation (3). ( I ¯ x ) = 4 , 266.67 + 124 , 245.333 + 124 , 245.333 = 252 , 757 mm 2 Find the moment of inertia ( I ¯ y ) 1 using the relation as shown below: ( I ¯ y ) 1 = 1 12 b 1 3 h 1 (4) Substitute 100 mm for b 1 and 8 mm for h 1 in Equation (4). ( I ¯ y ) 1 = 1 12 ( 100 3 ) × 8 = 666 , 666.667 mm 4 Find the moment of inertia ( I ¯ y ) 2 and ( I ¯ y ) 3 using the relation as shown below: ( I ¯ y ) 2 = ( I ¯ y ) 3 = 1 12 b 2 3 h 2 + ( b d ) y ¯ 2 (5) Substitute 8 mm for b 2 , 46 mm for y ¯ 2 , and 32 mm for h 2 in Equation (5). ( I ¯ y ) 2 = ( I ¯ y ) 3 = 1 12 ( 8 ) 3 ( 32 ) + ( 8 × 32 ) ( 46 ) 2 = 1 , 365.333 + 541 , 696 = 543 , 061.3 mm 4 Find the total moment of inertia ( I ¯ y ) using the relation as shown below: ( I ¯ y ) = ( I ¯ y ) 1 + ( I ¯ y ) 2 + ( I ¯ y ) 3 (6) Substitute 666 , 666

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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 9.3, Problem 9.88P

To determine

Find the orientation of the principal axes at the origin and the corresponding value of moment of inertia.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.3, Problem 9.87P

Chapter 9.3, Problem 9.89P

Students have asked these similar questions

answer this as soon as possible, please.

A piston–cylinder device contains 50 kg of water at 250 kPa and 25°C. The cross-sectional area of the piston is 0.1 m2. Heat is now transferred to the water, causing part of it to evaporate and expand. When the volume reaches 0.26 m3, the piston reaches a linear spring whose spring constant is 100 kN/m. More heat is transferred to the water until the piston rises 20 cm more. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the work done during this process. The work done during this process is kJ.

A 4-m × 5-m × 7-m room is heated by the radiator of a steam-heating system. The steam radiator transfers heat at a rate of 10,000 kJ/h, and a 100-W fan is used to distribute the warm air in the room. The rate of heat loss from the room is estimated to be about 5000 kJ/h. If the initial temperature of the room air is 10°C, determine how long it will take for the air temperature to rise to 25°C. Assume constant specific heats at room temperature. The gas constant of air is R = 0.287 kPa·m3/kg·K (Table A-1). Also, cv = 0.718 kJ/kg·K for air at room temperature (Table A-2). Steam enters the radiator system through an inlet outside the room and leaves the system through an outlet on the same side of the room. The fan is labeled as W sub p w. The heat is given off by the whole system consisting of room, radiator and fan at the rate of 5000 kilojoules per hour. It will take 831 Numeric ResponseEdit Unavailable. 831 incorrect.s for the air temperature to rise to 25°C.

Chapter 9 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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.

Find the orientation of the principal axes at the origin and the corresponding value of moment of inertia.

Solution Summary: The author explains the orientation of the principal axes at the origin and the corresponding value of moment of inertia.

Concept explainers

Videos

Find the orientation of the principal axes at the origin and the corresponding value of moment of inertia.

Want to see the full answer?

Chapter 9 Solutions