Space limitations in the design of an aircraft limit the wall thickness of an aluminum torsion member to 2.0 mm for the top half of the cross section. For simplicity, a constant-thickness tube with mean diameter D = 40 mm is proposed (Figure P6.41a). In an attempt to increase the design torque and torsional stiffness by 30% each, the design is modified such that the bottom half of the circumference has a wall thickness of 4.0 mm (Figure P6.41b). The maximum allowable shear stress is 60 MPa. a. Compare the allowable torques and the stiffnesses for the two designs. b. Compare the shear stress in the 2-mm and 4-mm sections for the design in Figure P6.41b. c. Which cross section would you recommend? Why?

Space limitations in the design of an aircraft limit the wall thickness of an aluminum torsion member to 2.0 mm for the top half of the cross section. For simplicity, a constant-thickness tube with mean diameter D = 40 mm is proposed (Figure P6.41a). In an attempt to increase the design torque and torsional stiffness by 30% each, the design is modified such that the bottom half of the circumference has a wall thickness of 4.0 mm (Figure P6.41b). The maximum allowable shear stress is 60 MPa. a. Compare the allowable torques and the stiffnesses for the two designs. b. Compare the shear stress in the 2-mm and 4-mm sections for the design in Figure P6.41b. c. Which cross section would you recommend? Why?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

A hollow aluminum tube used is a roof structure has an outside diameter d2=70mm and inside diameter d1= 50mm. The tube is 2.5m long and the aluminum has a shear modulus of G=28 GPa. 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 max shear stress is 50MPa? b.) What diameter 'd' is required for a solid shaft to resist the same torque with the same maximum stress?
We have a grounded 2 cm in diameter steel shaft which is 10 cm in length connected to a rigid surface. This shaft is subject to the stresses at the tip point as given below; • Tmean = 100 Nm, Talternating= 50 Nm, • Mmean = 30 Nm, Malternating= 40 Nm, Fmean = 4 kN, Falternating = 6 kN. This shaft has minimum properties of Sy = 800 Mpa and Sut = 1000 Mpa. Assume; Kf for bending=D1.5, Kf for tension = 1.4, and Kfs for torsion = 1.8. Using Modified Goodman criterion what can you say about the shaft? a) Does it have an infinite life?
The LPG tank with an inner diameter of 420 mm and a wall thickness of 2.2 mm in the figure operates under an internal pressure ranging from zero to 3.2 MPa. Also, an axially variable torsional moment of Tmax=10 kNm and Tmin=3 kNm is applied to the tank. The tank made of hot rolled steel sheet operates at ambient temperature. Accordingly, calculate the fatigue safety of the tank for 50% reliability? (yield strenght=460 Mpa,tensile strenght=520 Mpa) Note=Since there is no notch effect in the cylindrical part of the tank, take all kf as 1. For 50% reliability, take kc = Axial * Torsion = 0.51. Take the size factor kb = 0.85.
Consider a one-element triangular mesh shown in Figure 2. The edge AC is fixed. The edge BC is subject to lin- early varying traction normal to the edge as shown in Figure 2. Assume plane-stress conditions with thickness 1 = 1 cm and Young's modulus E = 70 GPa and Poisson's ratio v = 0.3. 150 kN/m 50 kN/m C (0,0.3) B (0.4,0.3) a) Specify the boundary condi- tions. b) Construct the stiffness matrix. A (0,0) c) Calculate the global force ma- Figure 2: Triangular element. All coordinates are in meters. trix. d) Solve for the unknown displace- ments and compute the stress at (0.1, 0.2).
The circular cross-section, L=0.5m long console BC shaft in the figure is forced to twist with P1=2 kN, P2=8 kN due to the forces on the belts connected to the pulley C. The radius of the pulley is R=0.4m and its weight is W=3 kN. Calculate shaft diameter D based on the assumption of maximum shear stress (TRESCA). Yield strength of the shaft = 240MPa and safety factor is S=2 1 kasnak D 2R P2 |B kayış y
6.13 A brass rod is a firm fit inside a steel tube 2 cm inside diameter and 4 cm outside diameter when the materials are at 15°C. If the rod and tube are now heated to a temperature of 150° C, calculate the maximum stresses in the brass and steel. Take the coeffi- cient of expansion for steel and brass as 10.8 × 10-6 and 18 x 10-6 per °C respectively. For steel E = 200 GPa and for brass E = 85 GPa. Poisson's ratio for both = 1/3. Neglect longitudinal frictional forces between the rod and the tube. %3D eleo
5. (a) (b) (c) Koo D d An Aluminium alloy (6061-T6) circular tube (Fig.Q5) used for vehicle fittings is under axial compression. The tube has a length L = 5m, outer diameter D = 65mm and inner diameter d = 55mm. The Young's modulus of Aluminium alloy 6061-T6 is E= 68.9 GPa and yield strength ay = 276 MPa. Determine the buckling load with the Euler formula, assuming the tube to be pin-jointed at the two ends Determine the buckling load with the Euler formula, assuming the tube to be fixed at the two ends Assuming the tube to be pin-jointed at both ends, determine the length of the tube, below which the Euler formula is no longer valid Fig.Q5 L-
A steel ring at a room temperature has a radius of R, of 1.00 mm x 1.00 mm. One like to insert a bar of radius R, = 2.002 cm into the ring. The following data is known for steel: 2.00 cm and a cross section area • Young Modulus E = 2.00 × 1011 Pa. • Coefficient of length contraction a = 1.20 x 10-5 C-1 • Specific heat capacity c = 511 J.kg-1.C-1 • Mass density p= 8050 kg.m -3 (a) What is the amount of heat needed for heating the ring so that the rod can fitted into it. (b) Assume the rod is rigid, calculate the pressure on the surface of the rod as the steel cool down to the room temperature.
The L-shaped rigid bar shown is pin connected at C, welded to a rigid bar AB at point B, and rests on a composite bar at D. Rigid bar AB is attached to two identical rubber (G = 150 MPa) pads with the shown dimensions and having a thickness of 30 mm each. Meanwhile, composite bar DE is made of hollow aluminum (with outer diameter do and inner diameter di, E = 70 GPa) surrounding a solid steel rod (diameter = di, E = 200 GPa). Determine the maximum force P that can be applied to the rigid bar at B if the allowable normal stresses in aluminum and steel are 80 MPa and 200 MPa, respectively and the shear stress in rubber is 30 MPa.Use the following values:Parameters s = 135 mm x = 3.8 m y = 5.5 m do = 60 mm di = 35 mm
L1 PB 2 E2 L2 D2 Dimensions: L2 L1 D2 D1 17 mm 18 cm 23 cm 15 mm Problem Statement: The rod shown is subjected to loads of PR = 112 kN and Pe = 18 kN. Segments AB and BC have elastic moduli of E, = 206 GPa and E = 73 GPa. The rod has circular cross-sections, and the dimensions of the rod are given above. Find the overall change in length of the rod under this load. Assume: • The collar at B is rigid • Stress concentration effects may be neglected 2014 Michael Swanbom
Shown below is a rigid beam ABC that is connected by pinned connections to rod (1) at A, rod (2) at C, and pivots freely at B. Rod (1) is made of bronze (E=100GPA, a=16.9x10-6/°C) and is 24mm in diameter. Rod (2) is made of aluminum (E=70GPA, a=22.5x10-6/°C) and is 16mm in diameter. The bars are unstressed as shown at 25°C. The temperature of bar (2) is reduced to 10°C while the temperature of bar (1) is held constant. Find the normal stress in bars (1) and (2). 250mm (1) |이 B A 200mm 350mm 500mm (2)
A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 70 lb/ft^2 against the full area of the sign. The dimensions of the poles and sign are h1 = 16 ft, h2 = 7 ft, and b = 13 ft. To prevent buckling of the walls of the poles, the thickness t is specified as one tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7100 psi in the aluminum. Round your answer to two decimal places. d = ___ in. (b) Determine the minimum required diameter based upon an allowable shear stress of 2100 psi. Round your answer to two decimal places. d = ___ in.