Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 2, Problem 2.12.8P
A rigid bar ACB is supported on a fulcrum at C and loaded by a Force P at end B (see figure). Three identical wires made of an elasloplastic material (yield stress oYand modulus of elasticity E) resist tbe load P. Each wire has cross-sectional area A and length L.
(a) Determine the yield load PYand the corresponding yield displacement Syat point B.
(b) Determine the plastic load PPand the corresponding displacement &pat point B when the load just reaches the value PP.
(c) Draw a load-displacement diagram with the load P as ordinate and the displacement SBof point B as abscissa.
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Question 2 (40 Points)
Consider the following double pendulum-like system with links ₁ and 12. The angles 0 and & could have
angular velocities ėêk and êk, respectively, where ②k is a unit vector that points out of the page and is
perpendicular to x and y. They could also have angular accelerations Ök and êk. The angle is
defined relative to the angle 0. The link 12 is a spring and can extend or compress at a rate of 12. It can
also have a rate of extension or compression Ï2.
li
y
êr1
êe
12
χ
3
еф
er2
ده لج
1) Express the velocity of the mass in terms of the unit vectors ê0, êr1, êø, and êr2, and any
extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points)
2) Express the acceleration of the mass in terms of the unit vectors ê¤, ê×1, êp, and êÃ2, and any
extension/contraction of the links (e.g.,. İ; and Ï¿) (12 Points)
3) Express the velocity of the mass in terms of unit vectors î and ĵ that point in the x and y
directions, respectively. Also include the appropriate,…
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...
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