EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220100257063
Author: BEER
Publisher: YUZU
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Chapter 2.3, Problem 50P
The concrete post (Ec = 3.6 × 106) psi and αc = 5.5 × 10-6/°F) is reinforced with six steel bars, each of
Fig. P2.50
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Problem 2.35
The 5-ft concrete post is reinforced with six steel bars, each with a 7/8-in. diameter. Knowing
that
E,
= 29 x 106 psi and E.= 3.6 x 106 psi, determine the normal stresses in the steel and in the
%3D
concrete when a 200-kip axial centric force is applied to the post.
5 ft
10 in.
10 in.
Flg. P2.35
Three forces, each of magnitude P = 3 kN, are applied to the structure shown. Determine the cross-sectional area of the uniform portion of rod BE for which the normal stress in that portion is +100 MPa.
The cross-sectional area of the uniform portion of rod BE is mm2.
The 1.5 m concrete post is reinforced with six steel bars, eachwith 28 mm diameter. Knowing the Es = 200 GPa and Ec = 200 GPa,determine the normal stresses in the steel and concrete when a 1550 kN axialcentric force P is applied to the post.
Chapter 2 Solutions
EBK MECHANICS OF MATERIALS
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. 82PCh. 2.9 - Prob. 83PCh. 2.9 - Prob. 84PCh. 2.9 - Prob. 85PCh. 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. 88PCh. 2.9 - Prob. 89PCh. 2.9 - Show that for any given material, the ratio G/E of...Ch. 2.9 - Prob. 91PCh. 2.9 - Prob. 92PCh. 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. 99PCh. 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. 104PCh. 2.13 - Rod ABC consists of two cylindrical portions and...Ch. 2.13 - Prob. 106PCh. 2.13 - Prob. 107PCh. 2.13 - Prob. 108PCh. 2.13 - Each cable has a cross-sectional area of 100 mm2...Ch. 2.13 - Prob. 110PCh. 2.13 - Two tempered-steel bars, each 316 in. thick, are...Ch. 2.13 - Prob. 112PCh. 2.13 - Prob. 113PCh. 2.13 - Prob. 114PCh. 2.13 - Prob. 115PCh. 2.13 - Prob. 116PCh. 2.13 - Prob. 117PCh. 2.13 - Prob. 118PCh. 2.13 - Prob. 119PCh. 2.13 - For the composite bar in Prob. 2.111, determine...Ch. 2.13 - Prob. 121PCh. 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. 127RPCh. 2 - Prob. 128RPCh. 2 - Prob. 129RPCh. 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. 132RPCh. 2 - Prob. 133RPCh. 2 - The aluminum test specimen shown is subjected to...Ch. 2 - Prob. 135RP
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- The 1.5 m concrete post is reinforced with six steel bars, eachwith 28 mm diameter. Knowing the Es = 200 GPa and Ec = 200 GPa,determine the normal stresses in the steel and concrete when a 1550 kN axialcentric force P is applied to the post.arrow_forwardA spherical gas tank is fabricated by bolting together two thin-walled hemispherical shells with an inner diameter of 8 m. The gas is pressurized to 2.0 MPa. The shells have an allowable normal stress of 150 MPa, and the 25 mm-diameter bolts have an allowable normal stress of 250 MPa. (a) Determine the minimum thickness of the walls of the tank to the nearest mm. (b) Determine the minimum number of bolts to connect the hemispheres.arrow_forwardA fabric used in air-inflated structures is subjected to a biaxial loading that results in normal stresses ox = 18 ksi and oz = 24 ksi.Knowing that the properties of the fabric can be approximated as E = 12.6 x 10 psi and v = 0.34, determine the change in length of (a) side AB, (b) side BC, (c) diagonal AC.arrow_forward
- 5. A load of 7,000 N acts on the machine part shown in Fig. 5a. The machine part has a uniform thickness of 15 mm (i.e., 15-mm thickness in the z direction). Determine the normal and shear stresses acting at points H and K, which are shown in detail in Fig. 5b. For eachpoint, show these stresses on a stress element. Fig. 5a Fig. 5b 2.5 in. 400 mm 5.2kN-m 20 KN 7.5KN 2.0 inarrow_forward2.60 At room temperature (20°C) a 0.5-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 140°C, determine (a) the normal stress in the aluminum rod, (b) the change in length of the aluminum rod. 0.5 mm 300 mm 250 mm B Aluminum Stainless steel A = 2000 mm² E = 75 GPa a = 23 × 16-6/°C Fig. P2.60 A = 800 mm² E = 190 GPa a = 17.3 × 10-6/°Carrow_forwardI need answer within 20 minutes please please with my best wishesarrow_forward
- Example: A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is made of brass (E, = 105 GPa, a, = 20.9 × 10*/°C) and portion BC is made of aluminum (E, = 72 GPa, a, = 23.9 × 10*rC). Knowing that the rod is initially unstressed, determine (a) the normal stresses induced in portions AB and BC by a temperature rise of 42°C, (b) the corresponding deflection of point B. %3Darrow_forwardEXERCISE 4.2 1. Three long parallel wires equal in length are supporting a rigid bar connected at their bottoms as shown in Fig. 4.15. If the cross-sectional area of each wire is 100 mm, calculate the stresses in cach wire. Take E, = 100 GPa and E, = 200 GPa. (Ans. o, 25 MPa ; 0, = 50 MPa] 10 kN Fig. 4.15 Brassarrow_forward1. A steel rod of 20 mm diameter passes centrally through a copper tube of external diameter 40 mm and internal diameter 20 mm. The tube is closed at each end with the help of rigid washers (of negligible thickness) which are screwed by the nuts. The nuts are tightened until the compressive load on the copper tube is 50 kN. Determine the stresses in the rod and the tube, when the temperature of whole assembly falls by 50°C. Take Es = 200 GPa ; Ec = 100 GPa ; as = 12 x 10-6/°C and ac = 18 x 106/°C.arrow_forward
- 2.49 A steel railroad track (E= 200 GPa, a = 11.7 × 10/°C) was laid out at a temperature of 6°C. Determine the normal stress in the rails when the temperature reaches 48 °C, assuming that the rails (a) are welded to form a continuous track, (b) are 10 m long with 3-mm gaps between them. PROBLEM 2.49 SOLUTIONarrow_forwardI need the answer as soon as possiblearrow_forwardQ.3. A steel rod of 20-mm diameter passes through a 0.8-m long brass tube of 35-mm external diameter and 25-mm internal diameter. The tube is closed at each end by rigid washers and nuts screwed to the rod. The nuts are tightened till the compressive force in the brass tube is 20 kN. Determine the stresses in the rod and tube. Given, Es= 200 GPa, Ee= 100 GPa [. [ Ans - o, = 31.8 MPa, o.= 21.2 MPa]arrow_forward
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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