(a) Explanation Given information: The diameter ( d A B ) of portion AB is 1.5 in . The diameter ( d B C ) of portion BC is 1 in . The diameter ( d C D ) of portion CD is 1.5 in . The length ( L A B ) of portion AB is 2 in . The length ( L B C ) of portion AB is 3 in . The length ( L C D ) of portion AB is 2 in . The total deformation ( δ ) is 0.002 in . Calculation: Show the expression of deformation to find the area as shown below: δ = ∑ P i L i A i E i = P E ∑ L i A i P = E δ ( ∑ L i A i ) − 1 A i = π 4 d i 2 Find the area ( A A B ) of portion AB using the relation as follows: ( A A B ) = π 4 ( d A B 2 ) (1) Substitute 1.5 in . for d A B in Equation (1). ( A A B ) = π 4 ( 1.5 2 ) = 1.7671 Find the area ( A B C ) of portion BC using the relation as follows: ( A B C ) = π 4 ( d B C 2 ) (2) Substitute 1.0 in . for d B C in Equation (2) (b) To determine Find the deformation of the central portion BC .

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external f…

Videos

Question

Chapter 2, Problem 128RP

(a)

To determine

Find the load P when total deformation is 0.002 in.

(b)

To determine

Find the deformation of the central portion BC.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 127RP

Chapter 2, Problem 129RP

Students have asked these similar questions

! Required information A telephone cable is clamped at A to the pole AB. The tension in the left-hand portion of the cable is given to be T₁ = 815 lb. A 15° 25° B T₂ Using trigonometry, determine the required tension T₂ in the right-hand portion if the resultant R of the forces exerted by the cable at A is to be vertical. The required tension is lb.

What are examples of at least three (3) applications of tolerance fitting analysis.

The primary material used in the production of glass products is silica sand. True or False

Chapter 2 Solutions

Mechanics of Materials, 7th Edition

Ch. 2.1 - A nylon thread is subjected to a 8.5-N tension...Ch. 2.1 - A 4.8-ft-long steel wire of 14 -in.-diameter is...Ch. 2.1 - An 18-m-long steel wire of 5-mm diameter is to be...Ch. 2.1 - Two gage marks are placed exactly 250 mm apart on...Ch. 2.1 - An aluminum pipe must not stretch more than 0.05...Ch. 2.1 - A control rod made of yellow brass must not...Ch. 2.1 - A steel control rod is 5.5 ft long and must not...Ch. 2.1 - A cast-iron tube is used to support a compressive...Ch. 2.1 - A 4-m-long steel rod must not stretch more than 3...Ch. 2.1 - A nylon thread is to be subjected to a 10-N...

Ch. 2.1 - A block of 10-in. length and 1.8 1.6-in. cross...Ch. 2.1 - A square yellow-brass bar must not stretch more...Ch. 2.1 - Rod BD is made of steel (E = 29 106 psi) and is...Ch. 2.1 - The 4-mm-diameter cable BC is made of a steel with...Ch. 2.1 - A single axial load of magnitude P = 15 kips is...Ch. 2.1 - A 250-mm-long aluminum tube (E = 70 GPa) of 36-mm...Ch. 2.1 - The specimen shown has been cut from a...Ch. 2.1 - The brass tube AB (E = 105 GPa) has a...Ch. 2.1 - Both portions of the rod ABC are made of an...Ch. 2.1 - The rod ABC is made of an aluminum for which E =...Ch. 2.1 - For the steel truss (E = 200 GPa) and loading...Ch. 2.1 - For the steel truss (E = 29 106 psi) and loading...Ch. 2.1 - Members AB and BC are made of steel (E = 29 106...Ch. 2.1 - The steel frame (E = 200 GPa) shown has a diagonal...Ch. 2.1 - Link BD is made of brass (E = 105 GPa) and has a...Ch. 2.1 - Members ABC and DEF are joined with steel links (E...Ch. 2.1 - Each of the links AB and CD is made of aluminum (E...Ch. 2.1 - The length of the 332-in.-diameter steel wire CD...Ch. 2.1 - A homogenous cable of length L and uniform cross...Ch. 2.1 - The vertical load P is applied at the center A of...Ch. 2.1 - Denoting by the "engineering strain'' in a...Ch. 2.1 - The volume of a tensile specimen is essentially...Ch. 2.3 - An axial centric force of magnitude P = 450 kN is...Ch. 2.3 - An axial centric force of magnitude P = 450 kN is...Ch. 2.3 - The 4.5-ft concrete post is reinforced with six...Ch. 2.3 - The 4.5-ft concrete post is reinforced with six...Ch. 2.3 - An axial force of 200 kW is applied to the...Ch. 2.3 - The length of the assembly shown decreases by 0.40...Ch. 2.3 - A polystyrene rod consisting of two cylindrical...Ch. 2.3 - Three steel rods (E = 29 106 psi) support an...Ch. 2.3 - Fig. P2.41 2.41 Two cylindrical rods, one of steel...Ch. 2.3 - Solve Prob. 2.41, assuming that rod AC is made of...Ch. 2.3 - Each of the rods BD and CE is made of brass (E =...Ch. 2.3 - The rigid bar AD is supported by two steel wires...Ch. 2.3 - The rigid bar ABC is suspended from three wines of...Ch. 2.3 - The rigid bar AD is supported by two steel wires...Ch. 2.3 - The aluminum shell is fully bonded to the brass...Ch. 2.3 - The aluminum shell is fully bonded to the brass...Ch. 2.3 - The brass shell (b = 11.6 10-6/F) is fully bonded...Ch. 2.3 - The concrete post (Ec = 3.6 106) psi and c = 5.5 ...Ch. 2.3 - A rod consisting of two cylindrical portions AB...Ch. 2.3 - A rod consisting of two cylindrical portions AB...Ch. 2.3 - Fig. P2.52 2.52 A rod consisting of two...Ch. 2.3 - The steel rails of a railroad (rack (Es = 200GPa,...Ch. 2.3 - Two steel bars (Es = 200 GPa and s = 11.7 10-6/C)...Ch. 2.3 - Determine the maximum load P that can be applied...Ch. 2.3 - An aluminum rod (Ea = 70 GPa, a = 23.6 10-6/C)...Ch. 2.3 - Knowing that a 0.02-in. gap exists when the...Ch. 2.3 - Determine (a) the compressive force in the bars...Ch. 2.3 - At room temperature (20C) a 0.5-mm gap exists...Ch. 2.9 - A standard tension test is used to determine the...Ch. 2.9 - A 2-m length of an aluminum pipe of 240-nun outer...Ch. 2.9 - A line of slope 4:10 has been scribed on a...Ch. 2.9 - A 2.75-kN tensile load is applied to a test coupon...Ch. 2.9 - Fig. P2.65 2.65 In a standard tensile test a steel...Ch. 2.9 - The change in diameter of a large steel bolt is...Ch. 2.9 - The brass rod AD is fitted with a jacket that is...Ch. 2.9 - A fabric used in air-inflated structures is...Ch. 2.9 - A 1-in. square was scribed on the side of a large...Ch. 2.9 - The block shown is made of a magnesium alloy for...Ch. 2.9 - The homogeneous plate ABCD is subjected to a...Ch. 2.9 - For a member under axial loading, express the...Ch. 2.9 - In many situations it is known that the normal...Ch. 2.9 - In many situations physical constraints prevent...Ch. 2.9 - The plastic block shown is bonded to a rigid...Ch. 2.9 - The plastic block shown is bonded to a rigid...Ch. 2.9 - Two blocks of rubber with a modulus of rigidity G...Ch. 2.9 - Fig. P2.77 and P2.78 2.78 Two blocks of rubber...Ch. 2.9 - An elastomeric bearing (G = 130 psi) is used to...Ch. 2.9 - 2.80 For the elastomeric bearing In Prob. 2.79...Ch. 2.9 - A vibration isolation unit consists of two blocks...Ch. 2.9 - Prob. 82P Ch. 2.9 - Prob. 83P Ch. 2.9 - Prob. 84P Ch. 2.9 - Prob. 85P Ch. 2.9 - A 2.75-kN tensile load is applied to a test coupon...Ch. 2.9 - A vibration isolation support consists of a rod A...Ch. 2.9 - Prob. 88P Ch. 2.9 - Prob. 89P Ch. 2.9 - Show that for any given material, the ratio G/E of...Ch. 2.9 - Prob. 91P Ch. 2.9 - Prob. 92P Ch. 2.13 - Knowing that, for the plate shown, the allowable...Ch. 2.13 - Knowing that P = 38 kN, determine the maximum...Ch. 2.13 - A hole is to be drilled in the plate at A. The...Ch. 2.13 - Fig. P2.95 and P2.96 2.96 (a) For P = 13 kips and...Ch. 2.13 - 2.97 Knowing that the hole has a diameter of 9 mm,...Ch. 2.13 - For P = 100 kN, determine the minimum plate...Ch. 2.13 - Prob. 99P Ch. 2.13 - A centric axial force is applied to the steel bar...Ch. 2.13 - The cylindrical rod AB has a length L = 5 ft and a...Ch. 2.13 - Fig. P2.101 and P.102 2.102 The cylindrical rod AB...Ch. 2.13 - Rod AB is made of a mild steel that is assumed to...Ch. 2.13 - Prob. 104P Ch. 2.13 - Rod ABC consists of two cylindrical portions and...Ch. 2.13 - Prob. 106P Ch. 2.13 - Prob. 107P Ch. 2.13 - Prob. 108P Ch. 2.13 - Each cable has a cross-sectional area of 100 mm2...Ch. 2.13 - Prob. 110P Ch. 2.13 - Two tempered-steel bars, each 316 in. thick, are...Ch. 2.13 - Prob. 112P Ch. 2.13 - Prob. 113P Ch. 2.13 - Prob. 114P Ch. 2.13 - Prob. 115P Ch. 2.13 - Prob. 116P Ch. 2.13 - Prob. 117P Ch. 2.13 - Prob. 118P Ch. 2.13 - Prob. 119P Ch. 2.13 - For the composite bar in Prob. 2.111, determine...Ch. 2.13 - Prob. 121P Ch. 2.13 - Bar AB has a cross-sectional area of 1200 mm2 and...Ch. 2.13 - Bar AB has a cross-sectional area of 1200 mm2 and...Ch. 2 - The uniform wire ABC, of unstretched length 2l, is...Ch. 2 - The aluminum rod ABC (E = 10.1 106 psi), which...Ch. 2 - Two solid cylindrical rods are joined at B and...Ch. 2 - Prob. 127RP Ch. 2 - Prob. 128RP Ch. 2 - Prob. 129RP Ch. 2 - A 4-ft concrete post is reinforced with four steel...Ch. 2 - The steel rods BE and CD each have a 16-mm...Ch. 2 - Prob. 132RP Ch. 2 - Prob. 133RP Ch. 2 - The aluminum test specimen shown is subjected to...Ch. 2 - Prob. 135RP

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 load P when total deformation is 0.002 in .

Solution Summary: The author shows the expression of deformation to find the area as shown below.