Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 2, Problem 2.5.22P
A non prism elk- bar ABC made up of segments AB(length £,, cross-sectional area .Inland BC (length i-,, cross-sectional area A2) is fixed at end A and free al end C (see figure). The modulus of elasticity of the bar is E. A small gap of d intension s exists between the end of the bar and an elastic spring of length Lj and spring constant k3. If bar ABC only (not tin? spring} is subjected to temperature increase A3", determine the following.
(a) Write an expression for reaction forces R^ and RDif the elongation of /I BC exceeds gap length s.
(b) Find expressions for the displacements of points B and C if the elongation of ABC exceeds gap length s.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The 2-mass system shown below depicts a disk which rotates about its center and has rotational
moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring
with constant k₂ is attached to the disk at a distance from the center. The mass m has linear
displacement & and is subject to an external force u. When the system is at equilibrium, the spring
forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may
assume the small angle approximation which implies (i) that the springs and dampers remain in
their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the
edge of the disk can be approximated by d≈re.
Ө
K2
www
m
4
Cz
777777
Jo
Make the following assumptions when analyzing the forces and torques:
тв
2
0>0, 0>0, x> > 0, >0
Derive the differential equations of motion for this dynamic system. Start by sketching
LARGE and carefully drawn free-body-diagrams for the disk and the…
A linear system is one that satisfies the principle of superposition. In other words, if an input u₁
yields the output y₁, and an input u2 yields the output y2, the system is said to be linear if a com-
bination of the inputs u = u₁ + u2 yield the sum of the outputs y = y1 + y2.
Using this fact, determine the output y(t) of the following linear system:
given the input:
P(s) =
=
Y(s)
U(s)
=
s+1
s+10
u(t) = e−2+ sin(t)
=e
The manometer fluid in the figure given below is mercury where D = 3 in and h = 1 in. Estimate the volume flow in the tube (ft3/s) if the flowing fluid is gasoline at 20°C and 1 atm. The density of mercury and gasoline are 26.34 slug/ft3 and 1.32 slug/ft3 respectively. The gravitational force is 32.2 ft/s2.
Chapter 2 Solutions
Mechanics of Materials (MindTap Course List)
Ch. 2 - A 10-ft rigid bar AB is supported with a vertical...Ch. 2 - Rigid bar ABC is supported with a pin at A and an...Ch. 2 - The L-shaped arm ABCD shown in the figure lies in...Ch. 2 - A steel cable with a nominal diameter of 25 mm...Ch. 2 - A steel wire- and an aluminum allay wire have...Ch. 2 - By what distance h does the cage shown in the...Ch. 2 - Rigid bar ACB is supported by an elastic circular...Ch. 2 - A plastic cylinder is held snugly between a rigid...Ch. 2 - A safety valve on the top of a tank containing...Ch. 2 - The device shown in the figure consists of a...
Ch. 2 - A small lab scale has a rigid L-shaped frame ABC...Ch. 2 - A small lab scale has a rigid L-shaped frame ABC...Ch. 2 - Two rigid bars are connected to each other by two...Ch. 2 - The three-bar truss ABC shown in the figure part a...Ch. 2 - An aluminum wire having a diameter d = 1/10 in....Ch. 2 - A uniform bar AB of weight W = 25 N is supported...Ch. 2 - A hollow, circular, cast-iron pipe (Ec =12,000...Ch. 2 - The horizon Lai rigid beam A BCD is supported by...Ch. 2 - Two pipe columns (AB, FC) are pin-connected to a...Ch. 2 - A framework ABC consists of two rigid bars AB and...Ch. 2 - Solve the preceding problem for the following...Ch. 2 - The length of the end segments of the bar (see...Ch. 2 - A long, rectangular copper bar under a tensile...Ch. 2 - An aluminum bar AD (see figure) has a...Ch. 2 - A vertical bar consists of three prismatic...Ch. 2 - A vertical bar is loaded with axial loads at...Ch. 2 - Repeat Problem 2.3-4, but now include the weight...Ch. 2 - -7 Repeat Problem 2.3-5, but n include the weight...Ch. 2 - A rectangular bar of length L has a slot in the...Ch. 2 - Solve the preceding problem if the axial stress in...Ch. 2 - A two-story building has steel columns AB in the...Ch. 2 - A steel bar is 8.0 Ft long and has a circular...Ch. 2 - A bar ABC of length L consists of two parts of...Ch. 2 - A woodpile, driven into the earth, supports a load...Ch. 2 - Consider the copper lubes joined in the strength...Ch. 2 - The nonprismalic cantilever circular bar shown has...Ch. 2 - *16 A prismatic bar AB of length L,...Ch. 2 - A flat bar of rectangular cross section, length L,...Ch. 2 - A flat brass bar has length L, constant thickness...Ch. 2 - Repeat Problem 2.3-18, but assume that the bar is...Ch. 2 - Repeat Problem 2.3-18, but assume that the bar is...Ch. 2 - A slightly tapered bar AB of solid circular crass...Ch. 2 - A circular aluminum alloy bar of length L = 1.8 m...Ch. 2 - A long, slender bar in the shape of a right...Ch. 2 - A post AB supporting equipment in a laboratory is...Ch. 2 - The main cables of a suspension bridge (see figure...Ch. 2 - A uniformly tapered lube AB of circular cross...Ch. 2 - A vertical steel bar ABC is pin-supported at its...Ch. 2 - A T-frame structure is torn posed of a prismatic...Ch. 2 - A T-frame structure is composed of prismatic beam...Ch. 2 - Repeat Problem 2.3-29 if vertical load P at D is...Ch. 2 - A bar ABC revolves in a horizontal plane about a...Ch. 2 - The assembly shown in the figure consists of a...Ch. 2 - A cylindrical assembly consisting of a brass core...Ch. 2 - A steel bar with a uniform cross section, is fixed...Ch. 2 - A horizontal rigid bar ABC is pinned at end A and...Ch. 2 - A solid circular steel cylinder S is encased in a...Ch. 2 - Three prismatic bars, two of material A and one of...Ch. 2 - A circular bar ACB of a diameter d having a...Ch. 2 - Bar ABC is fixed at both ends (see figure) and has...Ch. 2 - Repeat Problem 2.4-8, but assume that the bar is...Ch. 2 - A plastic rod AB of length L = 0.5 m has a...Ch. 2 - 2.4-11 Three steel cables jointly support a load...Ch. 2 - The fixed-end bar ABCD consists of three prismatic...Ch. 2 - A lube structure is acted on by loads at B and D,...Ch. 2 - A hollow circular pipe (see figure} support s a...Ch. 2 - The aluminum and steel pipes shown in the figure...Ch. 2 - A rigid bar of weight W = SOO N hangs from three...Ch. 2 - A bimetallic bar (or composite bar) of square...Ch. 2 - S Three-bar truss ABC (see figure) is constructed...Ch. 2 - A horizontal rigid bar of weight If' = 72001b is...Ch. 2 - A rigid bar ABCD is pinned at point B and...Ch. 2 - A rigid bar AB if of a length B = 66 in. is....Ch. 2 - Find expressions For all support reaction forces...Ch. 2 - A trimetallic bar is uniformly compressed by an...Ch. 2 - Find expressions for all support reaction Forces...Ch. 2 - The rails of a railroad track are welded together...Ch. 2 - A circular steel rod of diameter d is subjected to...Ch. 2 - A rigid bar of weight W = 750 lb hangs from three...Ch. 2 - A steel rod. of 15-mm diameter is held snugly (but...Ch. 2 - A bar AB of length L is held between rigid...Ch. 2 - A beam is constructed using two angle sections (L...Ch. 2 - A W 8 × 28 beam of a length 10 ft is held between...Ch. 2 - A plastic bar ACB having two different solid...Ch. 2 - ,5-9 A flat aluminum alloy bar is fixed at both...Ch. 2 - Repeat Problem 2.5-9 for the flat bar shown in the...Ch. 2 - A circular steel rod AB? (diameter d, = 1.0 in.,...Ch. 2 - A circular, aluminum alloy bar of a length L = 1.8...Ch. 2 - Rectangular bars of copper and aluminum are held...Ch. 2 - A brass sleeve S is fitted over a steel bolt B...Ch. 2 - A rigid triangular frame is pivoted at C and held...Ch. 2 - ,5-16 A rigid bar ABCD is pinned at end A and...Ch. 2 - A copper bar AB with a length 25 in. and diameter...Ch. 2 - A steel wire AB is stretched between rigid...Ch. 2 - -19 The mechanical assembly shown in the figure...Ch. 2 - A bar AB having a length L and axial rigidity EA...Ch. 2 - Pipe 2 has been inserted snugly into Pipe I. but...Ch. 2 - A non prism elk- bar ABC made up of segments...Ch. 2 - Wires B and C are attached to a support at the...Ch. 2 - A rigid steel plate is supported by three posts of...Ch. 2 - A capped cast-iron pipe is compressed by a brass...Ch. 2 - A plastic cylinder is held snugly between a rigid...Ch. 2 - Prob. 2.5.27PCh. 2 - Consider the sleeve made From two copper tubes...Ch. 2 - A polyethylene tube (length L) has a cap that when...Ch. 2 - Prestressed concrete beams are sometimes...Ch. 2 - Prob. 2.5.31PCh. 2 - A steel bar of rectangular cross section (1.5 in....Ch. 2 - A circular steel rod of diameter d is subjected to...Ch. 2 - A standard brick (dimensions 8 in. × 4 in. × 2.5...Ch. 2 - A brass wire of diameter d = 2.42 mm is stretched...Ch. 2 - Prob. 2.6.5PCh. 2 - A steel bar with a diameter d = 12 mm is subjected...Ch. 2 - During a tension lest of a mild-steel specimen...Ch. 2 - A copper bar with a rectangular cross section is...Ch. 2 - A prismatic bar with a length L = 3 ft and...Ch. 2 - A prismatic bar with a length L = 1 m and...Ch. 2 - The plane truss in the figure is assembled From...Ch. 2 - Plastic bar of diameter d = 32 mm is compressed in...Ch. 2 - A plastic bar of rectangular cross section (ft =...Ch. 2 - A copper bar of rectangular cross section (b = 18...Ch. 2 - A circular brass bar with a diameter J is member...Ch. 2 - Two boards are joined by gluing along a scarf...Ch. 2 - Acting on the sides of a stress element cut from a...Ch. 2 - A prismatic bar is subjected to an axial force...Ch. 2 - The normal stress on plane pq of a prismatic bar...Ch. 2 - A tension member is to be constructed of two...Ch. 2 - -21 Plastic bar AB of rectangular cross section (6...Ch. 2 - A compression bar having a square cross section...Ch. 2 - A prismatic bar AD of length L, cross-sectional...Ch. 2 - A bar with a circular cross section having two...Ch. 2 - A three-story steel column in a building supports...Ch. 2 - The bar ABC shown in the figure is loaded by a...Ch. 2 - Determine the strain energy per unit volume (units...Ch. 2 - The truss ABC shown in the Figure is subjected to...Ch. 2 - -7 The truss A BC Shawn in the figure supports a...Ch. 2 - The statically indeterminate structure shown in...Ch. 2 - A slightly tapered bar AB of rectangular cross...Ch. 2 - A compressive load P is transmitted through a...Ch. 2 - A block B is pushed against three springs by a...Ch. 2 - A bungee cord that behaves linearly elastically...Ch. 2 - A sliding collar of weight W = 150 lb falls From a...Ch. 2 - Solve the preceding problem if the collar has mass...Ch. 2 - Prob. 2.8.3PCh. 2 - A block weighing W = 5.0 N drops inside a cylinder...Ch. 2 - Solve the preceding problem for W = 1.0 lb. h = 12...Ch. 2 - Prob. 2.8.6PCh. 2 - A weight W = 4500 lb falls from a height h onto a...Ch. 2 - Prob. 2.8.8PCh. 2 - Prob. 2.8.9PCh. 2 - A bumping post at the end of a track in a railway...Ch. 2 - A bumper for a mine car is constructed with a...Ch. 2 - A bungee jumper having a mass of 55 kg leaps from...Ch. 2 - Prob. 2.8.13PCh. 2 - A rigid bar AB having a mass M = 1.0 kg and length...Ch. 2 - The flat bars shown in parts a and b of the figure...Ch. 2 - The flat bars shown in parts a and b of the figure...Ch. 2 - A flat bar of width b and thickness t has a hole...Ch. 2 - Around brass bar of a diameter d1= 20mm has upset...Ch. 2 - Prob. 2.10.5PCh. 2 - ,10-6 A prismatic bar with a diameter d0= 20 mm is...Ch. 2 - A stepped bar with a hole (see figure) has widths...Ch. 2 - A bar AB of length L and weight density y hangs...Ch. 2 - A prismatic bar of length L = 1.8 m and...Ch. 2 - Prob. 2.11.3PCh. 2 - A prismatic bar in tension has a length L = 2.0 m...Ch. 2 - An aluminum bar subjected to tensile Forces P has...Ch. 2 - A rigid bar AB is pinned al end A and is supported...Ch. 2 - Two identical bars AB and BC support a vertical...Ch. 2 - A stepped bar ACB with circular cross sections is...Ch. 2 - A horizontal rigid bar AB supporting a load P is...Ch. 2 - Prob. 2.12.4PCh. 2 - The symmetric truss ABCDE shown in the figure is...Ch. 2 - Five bars, each having a diameter of 10 mm....Ch. 2 - Prob. 2.12.7PCh. 2 - A rigid bar ACB is supported on a fulcrum at C and...Ch. 2 - The structure shown in the figure consists of a...Ch. 2 - Two cables, each having a length i. of...Ch. 2 - A hollow circular tube T of a length L = 15 in. is...
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
- Using the Bernoulli equation to find the general solution. If an initial condition is given, find the particular solution. y' + xy = xy¯¹, y(0) = 3arrow_forwardTest for exactness. If exact, solve. If not, use an integrating factor as given or obtained by inspection or by the theorems in the text. a. 2xydx+x²dy = 0 b. (x2+y2)dx-2xydy = 0 c. 6xydx+5(y + x2)dy = 0arrow_forwardNewton's law of cooling. A thermometer, reading 5°C, is brought into a room whose temperature is 22°C. One minute later the thermometer reading is 12°C. How long does it take until the reading is practically 22°C, say, 21.9°C?arrow_forward
- Solve a. y' + 2xy = ex-x² b. y' + y sin x = ecosx, y(0) = −1 y(0) = −2.5arrow_forward= MMB 241 Tutorial 3.pdf 2/6 90% + + 5. The boat is traveling along the circular path with a speed of v = (0.0625t²) m/s, where t is in seconds. Determine the magnitude of its acceleration when t = 10 s. 40 m v = 0.0625² 6. If the motorcycle has a deceleration of at = (0.001s) m/s² and its speed at position A is 25 m/s, determine the magnitude of its acceleration when it passes point B. .A 90° 300 m n B 2arrow_forward= MMB 241 Tutorial 3.pdf 4/6 67% + 9. The car is traveling along the road with a speed of v = (2 s) m/s, where s is in meters. Determine the magnitude of its acceleration when s = 10 m. v = (2s) m/s 50 m 10. The platform is rotating about the vertical axis such that at any instant its angular position is u = (4t 3/2) rad, where t is in seconds. A ball rolls outward along the radial groove so that its position is r = (0.1+³) m, where t is in seconds. Determine the magnitudes of the velocity and acceleration of the ball when t = 1.5s.arrow_forward
- The population of a certain country is known to increase at a rate proportional to the number of people presently living in the country. If after two years the population has doubled, and after three years the population is 20,000, estimate the number of people initially living in the country.arrow_forward= MMB 241 Tutorial 3.pdf 6/6 100% + | 日 13. The slotted link is pinned at O, and as a result of the constant angular velocity *= 3 rad/s it drives the peg P for a short distance along the spiral guide r = (0.40) m, where 0 is in radians. Determine the radial and transverse components of the velocity and acceleration of P at the instant = 1/3 rad. 0.5 m P r = 0.40 =3 rad/sarrow_forward= MMB 241 Tutorial 3.pdf 1/6 90% + DYNAMICS OF PARTICLES (MMB 241) Tutorial 3 Topic: Kinematics of Particles:- Path and Polar coordinate systems and general curvilinear QUESTIONS motion. 1. Determine the acceleration at s = 2 m if v = (2 s) m/s², where s is in meters. At s = 0, v = 1 m/s. 3 m 2. Determine the acceleration when t=1s if v = (4t2+2) m/s, where t is in seconds. v=(4²+2) m/s 6 marrow_forward
- 5.112 A mounting bracket for electronic components is formed from sheet metal with a uniform thickness. Locate the center of gravity of the bracket. 0.75 in. 3 in. ༧ Fig. P5.112 1.25 in. 0.75 in. y r = 0.625 in. 2.5 in. 1 in. 6 in. xarrow_forward4-105. Replace the force system acting on the beam by an equivalent resultant force and couple moment at point B. A 30 in. 4 in. 12 in. 16 in. B 30% 3 in. 10 in. 250 lb 260 lb 13 5 12 300 lbarrow_forwardSketch and Describe a hatch coaming and show how the hatch coamings are framed in to ships strucure?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Mechanical SPRING DESIGN Strategy and Restrictions in Under 15 Minutes!; Author: Less Boring Lectures;https://www.youtube.com/watch?v=dsWQrzfQt3s;License: Standard Youtube License