INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
14th Edition
ISBN: 9780133918922
Author: Russell C. Hibbeler
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 10.7, Problem 57P
Determine the product of inertia of the shaded area with respect to lire x and y axes, and then use the parallel-axis theorem to find the product of inertia of the area with respect to the centroidal x′ and y′ axes.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A bar of length L and of a circular cross-section of diameter D is clamped at the top end and loaded at the other (bottom) end by a point load P as shown in Figure
Q2a. The cross-section of the bar is shown in Figure Q2b indicating that load is applied at the point A. The material used in the bar has specific weight y.
Find the magnitude and location of the maximum normal stress in the bar.
Z
Figure Q2 a
Figure Q2 b
45°
A
A close end tube of thin-walled circular section may be subjected to torque Tand internal pressure P, as shown in Figure Q3. The shear stress in the wall caused by
the torque can be calculated as T = T/(2πR²t), where the mean radius of the cross section is R(i.e., the radius of the centreline of the wall) and the wall thickness
is t. The internal radius of the tube can be calculated as (R-t/2). However, as R>>t, you can approximately assume that the internal radius of the tube is equal to Rin
the subsequent calculation. The tube is made from a material with Young's modulus E, Poisson's ratio v.
T
Centreline of
the wall
R
P
Ozz
бөө
Orr
Z
бут
бее
Ozz
Figure Q3
(a) If the change of the diameter cannot exceed 0.1 m under elastic deformation, calculate the minimum allowable wall thickness of the cylindrical pressure vessel if
P=23.6 MPa, T=0 KN.m, R = 2 m, Young's modulus E = 246 GPa, and Poisson's ratio v = 0.21.
Step-1
the functional relationships between hoop stress σ and wall thickness…
A cantilever beam of a channel section and length L is loaded by a point load W applied at half-length of the beam through the centroid of the section, as shown in Figure Q1. The material of the beam is aluminum alloy with the Young’s modulus of E .
Chapter 10 Solutions
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
Ch. 10.3 - Determine the moment of inertia of the shaded area...Ch. 10.3 - Determine the moment of inertia of the shaded area...Ch. 10.3 - Determine the moment of inertia of the shaded area...Ch. 10.3 - Determine the moment of inertia of the shaded area...Ch. 10.3 - Determine the moment of inertia about the x axis.Ch. 10.3 - Determine the moment of inertia about the y axis.Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of Inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...
Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Solve the problem in two ways, using rectangular...Ch. 10.3 - Determine the moment of inertia of the area about...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia about the x axis.Ch. 10.3 - Determine the moment of inertia about the y axis.Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.3 - Prob. 23PCh. 10.3 - Determine the moment of inertia for the shaded...Ch. 10.4 - Determine the moment of inertia of the beams...Ch. 10.4 - Determine the moment of inertia of the beams...Ch. 10.4 - Determine me moment of inertia of the...Ch. 10.4 - Determine the moment of inertia of the...Ch. 10.4 - Determine the moment of inertia of the composite...Ch. 10.4 - Determine the moment of inertia of the composite...Ch. 10.4 - The moment of inertia about the y axis is 264...Ch. 10.4 - Determine the location y of the centroid of the...Ch. 10.4 - Determine,y, which locates the centroidal axis x...Ch. 10.4 - Determine the moment of inertia for the beams...Ch. 10.4 - Determine the moment of inertia for the beams...Ch. 10.4 - Determine the moment of inertia Ix of the shaded...Ch. 10.4 - Determine the moment of inertia Ix of the shaded...Ch. 10.4 - Determine the moment of inertia of the beams...Ch. 10.4 - Determine, g, which locates the centroidal axis z...Ch. 10.4 - Determine the moment of inertia about the x axis.Ch. 10.4 - Prob. 37PCh. 10.4 - Determine the moment of inertia of the shaded area...Ch. 10.4 - Determine the moment of inertia of the shaded area...Ch. 10.4 - Prob. 40PCh. 10.4 - Prob. 41PCh. 10.4 - Determine the moment of inertia of the beams...Ch. 10.4 - Prob. 43PCh. 10.4 - Prob. 44PCh. 10.4 - Determine the distance x to the centroid C of the...Ch. 10.4 - Determine the moment of inertia for the shaded...Ch. 10.4 - Determine the moment of inertia for the shaded...Ch. 10.4 - Determine the moment of inertia of the...Ch. 10.4 - Determine the moment of inertia of the...Ch. 10.4 - Prob. 50PCh. 10.4 - Determine the moment of inertia for the beams...Ch. 10.4 - Determine the moment of inertia of the area about...Ch. 10.4 - Determine the moment of inertia of the area about...Ch. 10.7 - Determine the product of inertia of the thin strip...Ch. 10.7 - Determine the product of inertia of the shaded...Ch. 10.7 - Determine the product of inertia for the shaded...Ch. 10.7 - Determine the product of inertia of the shaded...Ch. 10.7 - Determine the product of inertia for the parabolic...Ch. 10.7 - Prob. 59PCh. 10.7 - Determine the product of inertia of the shaded...Ch. 10.7 - Prob. 61PCh. 10.7 - Prob. 62PCh. 10.7 - Prob. 63PCh. 10.7 - Determine the product of inertia for the beams...Ch. 10.7 - Determine the product of inertia tor the shaded...Ch. 10.7 - Determine the product of inertia of the cross...Ch. 10.7 - Determine the location (xy) to the centroid C of...Ch. 10.7 - For the calculation, assume all comers to be...Ch. 10.7 - Determine the moments of inertia Iu, Iv and the...Ch. 10.7 - Prob. 70PCh. 10.7 - using Mohrs circle Hint. To solve find the...Ch. 10.7 - Prob. 72PCh. 10.7 - using Mohrs circle.Ch. 10.7 - Prob. 74PCh. 10.7 - using Mohrs circle.Ch. 10.7 - Prob. 76PCh. 10.7 - using Mohrs circle.Ch. 10.7 - Prob. 78PCh. 10.7 - using Mohrs circle.Ch. 10.7 - Prob. 80PCh. 10.7 - Solve Prob. 10-80 using Mohrs circle.Ch. 10.7 - Prob. 82PCh. 10.7 - Solve Prob. 10-82 using Mohrs circle.Ch. 10.8 - Determine the moment of inertia of the thin ring...Ch. 10.8 - The material has a constant density .Ch. 10.8 - Determine the radius of gyration kx of the...Ch. 10.8 - Prob. 87PCh. 10.8 - Hint: For integration, use thin plate elements...Ch. 10.8 - The material has a constant density .Ch. 10.8 - Prob. 90PCh. 10.8 - Determine the moment of inertia Iy. The specific...Ch. 10.8 - Prob. 92PCh. 10.8 - Prob. 93PCh. 10.8 - The total mass of the solid is 1500 kg.Ch. 10.8 - The slender rods have a mass of 4 kg/ point A....Ch. 10.8 - and a 4-kg slender rod. Determine the radius of...Ch. 10.8 - The material has a density of 200kg/m3. Prob....Ch. 10.8 - Determine the location y of the center of mass G...Ch. 10.8 - Prob. 99PCh. 10.8 - The pendulum consists of a plate having a weight...Ch. 10.8 - 15 lb. and 20 lb, respectively, determine the mass...Ch. 10.8 - The density of the material is 7.85 Mg/m3.Ch. 10.8 - Prob. 103PCh. 10.8 - Determine its mass moment of inertia about the y...Ch. 10.8 - Prob. 105PCh. 10.8 - Prob. 106PCh. 10.8 - Prob. 107PCh. 10.8 - The thin plate has a mass of 12 kg/m2. Determine...Ch. 10.8 - The material has a density of 200kg/m3.Ch. 10.8 - Determine the moment of inertia for the shaded...Ch. 10.8 - Determine the moment of inertia for the shaded...Ch. 10.8 - Determine the area moment of inertia of the shaded...Ch. 10.8 - Prob. 4RPCh. 10.8 - Determine the area moment of inertia of the...Ch. 10.8 - Determine the product of inertia of the shaded...
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.Similar questions
- A bar of length L and of a circular cross-section of diameter D is clamped at the top end and loaded at the other (bottom) end by a point load P as shown in Figure Q2a. The cross-section of the bar is shown in Figure Q2b indicating that load is applied at the point A. The material used in the bar has specific weight y. Find the magnitude and location of the maximum normal stress in the bar. Figure Q2 a Figure Q2 b 45°arrow_forwardQuestion2 The mission profile for a jet driven aircraft consists of the following segments: engine start and warm-up, taxi, take-off, climb to the cruise altitude of 35000 ft, descend to 10000 ft, one hour loiter at this altitude at 60% of the cruise speed, flight at loiter speed and altitude to an alternate airport (100 nm), descend to landing approach condition followed by the final landing, taxi and shutdown. The cruise Mach number is 0.8. No provisions are made for the reserved fuel or any trapped oil and fuel. The aircraft carries 200 people (including pilots and the cabin crew) at 175 lb each and 90 lb baggage each. This aircraft has a wing area of 2000 ft² a) If the landing stall speed of the aircraft is set at 100 kts corresponding to a landing weight of 0.85 Wro, and C(Lmax) Landing = 2.50, determine take-off weight and then calculate the range and empty weight of this aircraft (see Table Q2). Consider landing at sea level on a standard day. L/D at cruise L/D at 10000ft flight…arrow_forwardq Y X A ΕΙ L B Marrow_forward
- If L=3508 mm, W-9189 N, E=80 GPa, Determine the deflection at the free end of the beam. Step-1 The bend moment of the beam, M (Units: N.m), as a function of spatial coordinate X ( Units: m) can be described by Select one: O 1. M = 16117.506 +9189.000*X, for 0<=X<= L/2; M=0.00, for L/2< x <= L O 2. M = 16117506.000 - 9189.000*X, for 0<= x <= L/2; M = 9189.000* X, for L/2< x <= L O 3. M=16117.5069189.000*X, for 0<=X<= L/2; M=0.00, for L/2< x <= L O 4. M = 16117506.000 + 9189.000*X, for 0<=X<= L/2; M = 9189.000*X, for L/2arrow_forwardQuestion 1 A three-blade propeller of a diameter of 2 m has an activity factor AF of 200 and its ratio of static thrust coefficient to static torque coefficient is 10. The propeller's integrated lift coefficient is 0.3.arrow_forwardA close end tube of thin-walled circular section may be subjected to torque 7 and internal pressure P, as shown in Figure Q3. The shear stress in the wall caused by the torque can be calculated as T = T/(2πR²t), where the mean radius of the cross section is R (i.e., the radius of the centreline of the wall) and the wall thickness is t. The internal radius of the tube can be calculated as (R-t/2). However, as R>>t, you can approximately assume that the internal radius of the tube is equal to Rin the subsequent calculation. The tube is made from a material with Young's modulus E, Poisson's ratio v. Orr T t P Ozz бөө Orr Z T Ozz бед Figure Q3 Centreline of the wall R (a) If the change of the diameter cannot exceed 0.1 m under elastic deformation, calculate the minimum allowable wall thickness of the cylindrical pressure vessel if P=23.6 MPa, T=0 KN.m, R = 2 m, Young's modulus E = 246 GPa, and Poisson's ratio v = 0.21.arrow_forwardQuestion2 The mission profile for a jet driven aircraft consists of the following segments: engine start and warm-up, taxi, take-off, climb to the cruise altitude of 35000 ft, descend to 10000 ft, one hour loiter at this altitude at 60% of the cruise speed, flight at loiter speed and altitude to an alternate airport (100 nm), descend to landing approach condition followed by the final landing, taxi and shutdown. The cruise Mach number is 0.8. No provisions are made for the reserved fuel or any trapped oil and fuel. The aircraft carries 200 people (including pilots and the cabin crew) at 175 lb each and 90 lb baggage each. This aircraft has a wing area of 2000 ft² L/D at cruise L/D at 10000ft flight Table Q2 20 16 0.43 lb/hr/lb 0.50 lb/hr/lb C: Specific Fuel Consumption at cruise: C: Specific Fuel Consumption at 10000 ft flight: Weight ratios Engine Start and warm-up Taxi Take-off Climb Descent Landing, taxi and shutdown 0.992 0.996 0.996 0.996 0.992 0.992 Question 2 continues on the…arrow_forward[(a) If the change of the diameter cannot exceed 0.1 m under elastic deformation, calculate the minimum allowable wall thickness of the cylindrical pressure vessel. (P= 23.6 MPa, T=0 KN.m, R = 2 m, Young's modulus E = 246 GPa, and Poisson's ratio v = 0.21)] Step-4 The minimum allowable wall thickness of the cylindrical pressure vessel can be calculated as (Units: mm and rounded to three decimal places) Select one O 1.8.481 O 2.4.240 ○ 3.6.869 ○ 4. 16.961 5. 13.738 O 6.3.434arrow_forward[If L=3508 mm, W=9189 N, E=80 GPa, Determine the deflection at the free end of the beam.] Step -3 Which equation in the following choices most accurately represents the functional relationship between the value of the deflection v ( Units: mm) at half length (x =L/2) of the beam and the second moment of area about z-axis of the cross section, Izz ( Units: mm²): (Please note that " X = L/2" is the same as "X=L÷2".) Select one: O 1. v 588830960.433/Izz O 2. v=338836061.442/Izz O 3. v 119832265.632/Izz O 4. v 413214709.076/Izz O 5. v=287184222.808/Izz O 6. v=206607354.538/Izz O 7. v=66114353.452/Izz O 8. v 752050770.518/Izzarrow_forwardA bar of length L and of a circular cross-section of diameter D is clamped at the top end and loaded at the other (bottom) end by a point load P as shown in Figure Q2a. The cross-section of the bar is shown in Figure Q2b indicating that load is applied at the point A. The material used in the bar has specific weight y. Find the magnitude and location of the maximum normal stress in the bar. Figure Q2 a Figure Q2 b 45° A Step -1 The given load case can be represented by a statically equivalent system of the following loads Select one: O 1. A tensile force placed at the centroid with intensity equals to 0.354 P; a bending moment about zaxis, M₂ = (P×D× 0.708); a bending moment about yaxis, My= (Px D× 0.177); and self-weight of the vertical beam producing maximum tensile stress at the built-in end. ○ 2. A tensile force placed at the centroid with intensity equals to 0.354P; a bending moment about z axis, M₂ = (PxDx 0.354); a bending moment about yaxis, My= (Px D× 0.177); and self-weight…arrow_forwardQuestion 1 A three-blade propeller of a diameter of 2 m has an activity factor AF of 200 and its ratio of static thrust coefficient to static torque coefficient is 10. The propeller's integrated lift coefficient is 0.3. a) Calculate the static power and thrust coefficients.arrow_forwardA cantilever beam of a channel section and length L is loaded by a point load W applied at half-length of the beam through the centroid of the section, as shown in Figure Q1. The material of the beam is aluminum alloy with the Young's modulus of E. 1. As illustrated in Figure Q1, the Y-axis is positioned along the symmetric plane of the cross-section, while the Z-axis and X-axis pass through the centroid of the cross-section. The X-axis is defined using the right-hand rule, with the origin located at the fixed end. The distance from the centroid to the bottom of the cross- section, yc (Units: mm), is: Select one: O 1. 48.72 O 2. 70.24 ○ 3. 76.38 ○ 4. 83.12 O 5. 68.73 ○ 6. 50.26 ○ 7. 56.19 ○ 8. 88.73 ○ 9. 62.82 O 10. 42.83 W a a 25 mm y Z AN a-a 25 mm 150 mm SC yc 6 mm Figure Q 1 200 mmarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY