Problem 3.9 A shaft composed of segments AC, CD, and DB is fastened to rigid supports and loaded as shown in the figure. For bronze, G = 6 x 106 psi; aluminum, G = 4 x 10° psi; and for steel, G = 12 x 106 psi. Determine the maximum shearing stress developed in each segment!

Problem 3.9 A shaft composed of segments AC, CD, and DB is fastened to rigid supports and loaded as shown in the figure. For bronze, G = 6 x 106 psi; aluminum, G = 4 x 10° psi; and for steel, G = 12 x 106 psi. Determine the maximum shearing stress developed in each segment!

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.3.12P: A propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable...

See similar textbooks

Related questions

Q: 4. The solid shaft and tube shown in Figure are made of a material having an allowable shear stress…

Q: A flanged bolt coupling consists of ten 20-mm diameter steel bolts spaced evenly around a bolt…

Q: 3. A solid shaft is shown below. If d = 100 mm, 1 = 1 m, Me = 2n kN m, and the allowable shear…

Q: The butt joint shown in the figure is connected using five 20 mm diameter bolt. If the tension force…

Q: 2. A hollow shaft of 30-mm inner diameter and 60-mm outer diameter is acted on by an axial tensile…

Q: 3. The solid steel shaft AC (G= 80 GPa) is supported by smooth bearings at D and E as shown in…

Q: 4 kN m 1.5 kN m Aluminum Steel Bronze B 100 mm 75 mm 3m 2 m 1.5 m- C FIG. P3.12 FIG. P3.11 3.12 The…

A: For solution refer below images.

Q: A solid steel shaft in a rolling mill transmits 20 kW of power at 2 Hz. Determine the smallest safe…

Q: The compound shaft is attached to a rigid wall at each end. For the bronze segment AB, the diameter…

Q: Two shafts are being connected by a coupling which is held together by four 3/4-in diameter bolts.…

Q: Since each of the shafts AB, BC and CD shown in the figure consists of a solid circular bar,…

A: Given data: The diameter of the part AB is dAB=15 mm The diameter of the part BC is dBC=18 mm The…

Q: Will cause a shear stress of 6000 psi? 3.41 The constant wall thickness of a steel tube with the…

A: Given Radius, R = 10 mm Diameter, D = 20 mm Torque, T = 600 N. m Length, L = 30 mm Find…

Q: Problem 3.9 A shaft composed of segments AC, CD, and DB is fastened to rigid supports and loaded as…

Q: 3.6 Two forces, each of magnitude P, are applied to the wrench. The diameter of the steel shaft AB…

A: Diameter of the steel shaft AB, D= 15 mm Maximum allowable shear force in the shaft, τ= 120 MPa…

Q: The constant wall thickness of a steel tube with the cross section shown is 2 mm. If a 600-N m…

A: Given data: d=10 mmri=9 mmt=2 mmro=11 mmT=600 N.mG=80 GPa Need to determine the shear stress in the…

Q: 3.6 Two forces, each of magnitude P, are applied to the wrench. The diameter of the steel shaft AB…

Q: Fig. P3.52 and P3.53 PROBLEM 3.54 The composite shaft shown consists of a 5 mm thick brass jacket (G…

Q: 600 G0° 70 mm

Q: Problem 3.15. A hollow aluminium tube of rectangular cross- section as shown in Fig. 3.27 is…

A: We know that a hollow aluminum tube with a rectangular cross section is subjected to a torque of…

Q: H.W:The bell crank shown in Figure , is in equilibrium, a) Determine the required diameter of the…

A: Given :connecting rod=ABσxAB=100 MNm2

Q: espectively, is fixed on one end and torsional forces (T=10 kN.m) are applied at joining points as…

A: givensolid shaft made of steel aluminium and bronze length of each segments L=3m=3000mmtorsional…

Q: 2. An equilateral triangle pipe, as shown in the figure has a uniform thickness of 1.5 mm. The…

A: The section is an equilateral triangle. It is symmetrical . And thus the centroid lies on the plane…

Q: A cylindrical metal tube of mean radius r = 5 in., length L = 14 ft, and shear modulus G = 11 x 106…

Q: The wrench is applied to two forces each of magnitude P. The steel shaft AB has a diameter of 15 mm.…

Q: A solid bar having a diameter 150 mm is to be replaced by a square tube having a cross-sectional…

Q: Problem 3.9 A shaft composed of segments AC, CD, and DB is fastened to rigid support and loaded as…

Q: An aluminum alloy cylindrical roller with diameter 1.25 in and length 2 in rolls on the inside of a…

Q: Problem B-2 [Statically Indeterminant Problem – Torsional Loading] A solid compound circular shaft…

Q: Calculate the torque T: i. if the shear stress of the brass sleeve in section AB is limited to τb =…

A: Shear stress is defined as the intensity of force acting on the cross sectional area. Shear stress…

Q: 3.6 Two forces, each of magnitude P, are applied to the wrench. The diameter of the steel shaft AB…

A: Torque:

Q: 1.5 kN m 4 kN m Steel Aluminum Bronze 100 mm 75 mm 3 m 2 m -1.5 m- C FIG. P3.12 FIG. P3.11 3.12 The…

A: Answer: (a) Maximum shear stress in each material : ◆ Aluminum : 28.0 MPa. ◆ Steel and Bronze :…

Q: Q4-A circular shaft consists of steel and aluminum segments is subjected to the torques shown in…

Q: The butt joint shown in the figure is connected using five 20 mm diameter bolt. If the tension force…

Q: For the pin-connected structure in the figure, determine the minimum diameter for the pin at joint D…

Q: The composite shaft shown in the figure is manufactured by shrink-fitting a steel sleeve over a…

Q: Problem 2: A steel tube having an outer diameter of 2.5 in. is used to transmit 10 hp when turning…

A: Given:D=2.5 inP=10 hpN=30 rpmζallow=12 ksi

Q: Problem1: The entire composite shaft shown in the following figure is manufactured using steel with…

A: GivenG=80GPatorque =Tτa=75MPa

Q: 3.6 Two forces, each of magnitude P, are applied to the wrench. The diameter of the steel shaft AB…

A: Find the largest allowable value of P.

Q: . The shaft shown in the figure is made from a steel tube, which is bonded to a brass core. If a…

A: Let assume torque acting on steel is T1 and Torque acting on brass is T2 ,so T1+T2=227 , equation…

Q: A 28mm diameter steel shaft AB is built into a rigid wall at A and supported by a smooth bearing at…

Q: 45 mm B 60 mm 30 mm 2 m -1.2 m

Q: A solid 1.500-in.-diameter steel [G = 11,000 ksi] shaft is subjected to torques TB = 190 lb-ft and…

A: Given Datad=1.5inG=11,000ksiTB=190 lb-ftTD=140 lb-fta=42 inb=72 inc=36 in

Q: In the steel structure shown, a 6mm diameter pin is used at C and 10mm diameter pins are used at B…

A: Given data as per question Diameter of the pin at c =6 mm Diameter of the pin at B and D =10 mm…

Q: A flange-and-bolt coupling between two shafts carries 12 bolts at a pitch diameter of 18 in. The…

A: Given data: In a Flange and Bolt coupling between two shafts: Number of bolts, n=12. Pitch circle…

Q: 3.41 The constant wall thickness of a steel tube with the cross section shown is 2 mm. If a 600-N m…

Q: A shaft composed of segments AC, CD, and DB is fastened to rigid supports and loaded as shown in the…

Q: Compute the shearing stress if a torque T = 200 N-m is applied to a thin-walled tube having a cross…

Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

100%

Problem 3.9 A shaft composed of segments AC, CD, and DB is fastened to rigid supports
and loaded as shown in the figure. For bronze, G = 6 x 106 psi; aluminum, G =
4x 10° psi; and for steel, G = 12 x 106 psi. Determine the maximum shearing stress
developed in each segmenį
Tc = 250 lb – ft Td = 500 lb – ft
Aluminum
Steel
Bronze
A
1.0 in.
2 in.
$1.0 in.
D
(C
6 ft
4 ft - 3 ft

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

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 stepped shaft shown in the figure is required to transmit 600 kW of power at 400 rpm. The shaft has a full quarter-circular fillet, and the smaller diameter D1= 100 mm. If the allowable shear stress at the stress concentration is 100 MPa, at what diameter will this stress be reached? Is this diameter an upper or a lower limit on the value of D2?
A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (sec figure). If the allowable shear stress in the shaft is 6000 psi, what is the maximum torque (T0) that may be applied at section C? Find (T0)max if the maximum angle of twist is limited to 0.55º. Let G = 10,600 ksi.
A thin-walled steel tube having an elliptical cross section with constant thickness t (see figure) is subjected to a torque T = 18 kip-in. Determine the shear stress and the rate of twist in degrees per inch) if G = 12 × 106 psi, t = 0.2 in., a = 3 in., and b = 2 in. Note: See Appendix E, Case 16, for the properties of an ellipse.
A thin tubular shaft with a circular cross section (see figure) and with inside diameter 100 mm is subjected to a torque of 5000 N · m. If the allowable shear stress is 42 MPa, determine the required wall thickness t by using (a) the approximate theory for a thin-walled tube and (b) the exact torsion theory for a circular bar.
A solid copper bar of circular cross section has length L = 1.25 m and shear modulus of elasticity G = 45 GPa. The bar is designed to carry a 250 N · m torque acting at the ends. If the allowable shear stress is 30 M Pa and the allowable angle of twist between the ends is 2.5°, what is the minimum required diameter?
A thin-walled rectangular tube has uniform thickness t and dimensions a x b to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio = a/b if the total length Lmof the median line of the cross section and the torque T remain constant? From your results, show that the shear stress is smallest when the tube is square (ß = 1).
A circular aluminum tube subjected to pure torsion by torques T(sec figure) has an outer radius r2equal to 1.5 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 400 × 10-6 rad, what is the shear strain y1at the inner surface? (b) If the maximum a1lo-abk rate of twist is 0.125 °/m and the maximum shear strain is to be kept at 400 × 10-6 rad by adjusting the torque T, that is the minimum required outer radius ( r2)Min?
A hollow tube ABCDE constructed of monel metal is subjected to five torques acting in the directions shown in the figure. The magnitudes of the torques are T1= 1000 lb-in., T2= T4= 500 lb-in., and T3= T5= 800 lb-in. The tube has an outside diameter of d2= 1.0 in. The allowable shear stress is 12,000 psi and the allowable rate of twist is 2.0°/ft. Determine the maximum permissible inside diameter d1, of the tube.
A stepped shaft consisting of solid circular segments having diameters D1= 2.0 in, and D2= 2.4 in. (see figure) is subjected to torques T. The radius of the fillet is R = 0,1 in. If the allowable shear stress at the stress concentration is 6000 psi, what is the maximum permissible torque Tmax?
A copper tube with circular cross section has length L = 1.25 m, thickness t = 2 mm, and shear modulus of elasticity G = 45 GPa. The bar is designed to carry a 300 N·m torque acting at the ends. If the allowable shear stress is 25 MPa and the allowable angle of twist between the ends is 2.5°, what is the minimum required outer diameter d?
2. A hollow shaft and a solid shaft constructed of the same material have the same length and the same outer radius. The inner radius R of the hollow shaft is 0.6R. Assuming that both shafts are subjected to the same torque, compare their shear stresses, angle of twist and weights. 3. A hollow aluminium tube used in a roof structure has an outside diameter 104mm and an inside diameter 82mm. The tube is 2.75m long and the aluminium has shear modulus G=28GPa. a. If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist (in degrees) when the maximum shear stress is 48 MPa.b. What diameter d is required for a solid shaft to resist the same torque with the same maximum stress.c. What is the ratio of the weight of the hollow tube to the weight of the solid shaft?
Q2/A compound shaft shown in the figure is subjected to a torque TC = 7500 N.m at C and restrained by a support at A. Segment (1) is a solid brass [G1 = 5800 GPa] shaft with an allowable shear stress of τ1 = 38 MPa. Segment (2) is a solid aluminum [G2 = 4000 GPa] shaft with an allowable shear stressof τ2 = 69 MPa. [L1= 0.7 m, L2= 0.5 m] Determine the minimum required diameter of the brass shaft (1)?in mm Determine the minimum required diameter of the aluminum shaft (2)?