MECHANICS OF MATERIALS
10th Edition
ISBN: 2818440034374
Author: HIBBELER
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3.4, Problem 3.20P
The stress-strain diagram for a bone is shown and can be described by the equation ε = 0.45 (10−6) σ + 0.36 (10−12) σ3 where σ is in kPa. Determine the modulus of toughness and the amount of elongation of a 200-mm-long region just before it fractures if failure occurs at ε = 0.12 mm/mm.
Prob. 3–20
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A particle is held and then let go at the edge of a circular shaped hill of radius R =
shown below. The angular motion of the particle is governed by the following ODE:
+ 0.4 02 - 2 cos 0 + 0.8 sin 0 = 0
where is the angle in rad measured from the top (CCW: +), ė
5m, as
= wis the velocity in rad/s,
==a is the angular acceleration in rad/s². Use MATLAB to numerically integrate the
second order ODE and predict the motion of the particle.
(a) Plot and w vs. time
(b) How long does it take for the particle to fall off the ring at the bottom?
(c) What is the particle speed at the bottom. Hint v = Rw.
in de
all questions
the particles inside the tube.
/2/07/25
Particle
R
0
0
R
eled with
If FA = 40 KN and FB = 35 kN, determine the magnitude of
the resultant force and specify the location of its point of
application (x, y) on the slab.
30 kN
0.75 m
90 kN
FB 2.5 m
20 kN
2.5 m
0.75 m
FA
0.75 m
3 m
3 m
0.75 m
The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω 2 x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L.
Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).
Chapter 3 Solutions
MECHANICS OF MATERIALS
Ch. 3.4 - Define a homogeneous material.Ch. 3.4 - Indicate the points on the stress-strain diagram...Ch. 3.4 - Define the modulus of elasticity E.Ch. 3.4 - At room temperature, mild steel is a ductile...Ch. 3.4 - Engineering stress and strain are calculated using...Ch. 3.4 - As the temperature increases the modulus of...Ch. 3.4 - A 100-mm-long rod has a diameter of 15 mm. If an...Ch. 3.4 - A bar has a length of 8 in. and cross-sectional...Ch. 3.4 - A 10-mm-diameter rod has a modulus of elasticity...Ch. 3.4 - The material for the 50-mm-long specimen has the...
Ch. 3.4 - The material for the 50-mm-long specimen has the...Ch. 3.4 - If the elongation of wire BC is 0.2 mm after the...Ch. 3.4 - A tension test was performed on a steel specimen...Ch. 3.4 - Data taken from a stress-strain test for a ceramic...Ch. 3.4 - Data taken from a stress-strain test for a ceramic...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - The rigid beam is supported by a pin at C and an...Ch. 3.4 - The rigid beam is supported by a pin at C and an...Ch. 3.4 - Acetal plastic has a stress-strain diagram as...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - A bar having a length of 5 in. and cross-sectional...Ch. 3.4 - The rigid pipe is supported by a pin at A and an...Ch. 3.4 - The rigid pipe is supported by a pin at A and an...Ch. 3.4 - Direct tension indicators are sometimes used...Ch. 3.4 - The rigid beam is supported by a pin at C and an...Ch. 3.4 - The rigid beam is supported by a pin at C and an...Ch. 3.4 - The stress-strain diagram for a bone is shown, and...Ch. 3.4 - The stress-strain diagram for a bone is shown and...Ch. 3.4 - The two bars are made of a material that has the...Ch. 3.4 - The two bars are made of a material that has the...Ch. 3.4 - The pole is supported by a pin at C and an A-36...Ch. 3.4 - The bar DA is rigid and is originally held in the...Ch. 3.7 - A 100-mm-long rod has a diameter of 15 mm. If an...Ch. 3.7 - A solid circular rod that is 600 mm long and 20 mm...Ch. 3.7 - A 20-mm-wide block is firmly bonded to rigid...Ch. 3.7 - A 20-mm-wide block is bonded to rigid plates at...Ch. 3.7 - The acrylic plastic rod is 200 mm long and 15 mm...Ch. 3.7 - The plug has a diameter of 30 mm and fits within a...Ch. 3.7 - The elastic portion of the stress-strain diagram...Ch. 3.7 - The elastic portion of the stress-strain diagram...Ch. 3.7 - The brake pads for a bicycle tire are made of...Ch. 3.7 - The lap joint is connected together using a 1.25...Ch. 3.7 - The lap joint is connected together using a 1.25...Ch. 3.7 - The rubber block is subjected to an elongation of...Ch. 3.7 - The shear stress-strain diagram for an alloy is...Ch. 3.7 - A shear spring is made from two blocks of rubber,...Ch. 3 - The elastic portion of the tension stress-strain...Ch. 3 - The elastic portion of the tension stress-strain...Ch. 3 - The rigid beam rests in the horizontal position on...Ch. 3 - The wires each have a diameter of 12 in., length...Ch. 3 - The wires each have a diameter of 12 in., length...Ch. 3 - diameter steel bolts. If the clamping force in...Ch. 3 - The stress-strain diagram for polyethylene, which...Ch. 3 - The pipe with two rigid caps attached to its ends...Ch. 3 - The 8-mm-diameter bolt is made of an aluminum...Ch. 3 - An acetal polymer block is fixed to the rigid...
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
- The heated rod from Problem 3 is subject to a volumetric heatingh(x) = h0xLin units of [Wm−3], as shown in the figure below. Under theheat supply the temperature of the rod changes along x with thetemperature function T(x). The temperature T(x) is governed by thefollowing equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(4)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. Both ends of the bar are in contact with a heatreservoir at zero temperature. Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).arrow_forwardA heated rod of length L is subject to a volumetric heating h(x) = h0xLinunits of [Wm−3], as shown in the figure below. Under the heat supply thetemperature of the rod changes along x with the temperature functionT(x). The temperature T(x) is governed by the following equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(3)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. The left end of the bar is in contact with a heatreservoir at zero temperature, while the right end of the bar is thermallyinsulated. Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).arrow_forwardCalculate the mean piston speed (in mph) for a Formula 1 engine running at 14,750 rpm with a bore of 80mm and a stroke of 53mm. Estimate the average acceleration imparted on the piston as it moves from TDC to 90 degrees ATDCarrow_forward
- Calculate the compression ratio of an engine with a stroke of 4.2inches a bore of 4.5 inches and a clearance volume of 6.15 cubic inches. Discuss whether or not this is a realistic compression ratio for a street engine and what octane rating of fuel it would need to run correctlyarrow_forwardDraw the free-body diagram for the pinned assembly shown. Find the magnitude of the forces acting on each member of the assembly. 1500 N 1500 N C 45° 45° 45° 45° 1000 mmarrow_forwardAn elastic bar of length L spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω 2 x. Due to this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (1) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0, and it is free at x = L. Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).arrow_forward
- With reference to the given figure: a) Draw a free-body diagram of the structure supporting the pulley. b) Draw shear and bending moment diagrams for both the vertical and horizontal portions of the structure. 48 in. 100 lb 12 in. Cable 27 in. 12-in. pulley radius 100 lb Cablearrow_forwardConsider a standard piston engine . Draw a free body diagram of the piston. Then:a) For an A SI engine with a 100 mm bore at an instantaneous cylinder pressure of 42 bar i. Calculate the level of the combustion gas loading force on the wrist pin in kN. b) Repeat this calculationfor a forced-induction Diesel engine with a 145 mm boreat a cylinder pressure of 115 bararrow_forwardA punch press with flywheel adequate to minimize speed fluctuation produces 120 punching strokes per minute, each providing an average force of 2000 N over a stroke of 50 mm. The press is driven through a gear reducer by a shaft rotating 200 rpm. Overall efficiency is 80%. a) What power (W) is transmitted through the shaft? b) What average torque is applied to the shaft?arrow_forward
- 1.58 The crankshaft of a single-cylinder air compressor rotates 1800 rpm. The piston area is 2000 mm2 and the piston stroke is 50 mm. Assume a simple “idealized” case where the average gas pressure acting on the piston during the compression stroke is 1 MPa, and pressure during the intake stroke is negligible. The compressor is 80% efficient. A flywheel provides adequate control of the speed fluctuation. a) What motor power (kW) is required to drive the crankshaft? b) What torque is transmitted through the crankshaft?arrow_forward28. The shaft shown in Figure P5-28 is supported by bear- ings at each end, which have bores of 20.0 mm. Design the shaft to carry the given load if it is steady and the shaft is stationary. Make the dimension a as large as pos- sible while keeping the stress safe. Determine the required d 20 mm 5.4 kN d D = ? Length not to scale -α = = -125 mm 20 mm a = -250 mm- FIGURE P5-28 (Problems 28, 29, and 30)arrow_forwardThe motor shown operates at constant speed and develops a torque of 100 lb-in during normal operation. Attached to the motor shaft is a gear reducer of ratio 5:1, that is, the reducer output shaft rotates in the same direction as the motor but at one-fifth motor speed. Rotation of the reducer housing is prevented by the "torque arm" pin-connected at each end as shown. The reducer output shaft drives the load through a flexible coupling. Neglecting gravity and friction, what loads are applied to (a) the torque arm, (b) the motor output shaft, and (c) the reducer output shaft? Motor Gear reducer Flexible coupling (To load) Torque arm- Torque arm Reducer output shaft Motor Reducer Shaft rotationarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
EVERYTHING on Axial Loading Normal Stress in 10 MINUTES - Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=jQ-fNqZWrNg;License: Standard YouTube License, CC-BY