Mechanical Engineering Principles

92 MECHANICAL ENGINEERING PRINCIPLES Problem 8. Determine the second moment of area and radius of gyration about axisQQ of the t ...

FIRST AND SECOND MOMENT OF AREAS 93 Problem 11. Determine the second moment of area and radius of gyration for the semicircle sh ...

94 MECHANICAL ENGINEERING PRINCIPLES d Figure 7.17 The lamina is shown in Figure 7.17. From the perpendicular axis theorem: IZZ= ...

FIRST AND SECOND MOMENT OF AREAS 95 Determine the second moment of area and radius of gyration for the trian- gle shown in Figu ...

96 MECHANICAL ENGINEERING PRINCIPLES Determine the second moments of areas about the given axes for the shapes shown in Figure ...

FIRST AND SECOND MOMENT OF AREAS 97 0.1 m 0.1 m 0.1 m ab c d e f g h N A Figure 7.30 The centroid of this beam will be on the ho ...

98 MECHANICAL ENGINEERING PRINCIPLES Hence, i 1 = 0. 1 × 0. 023 12 = 6. 6 × 10 −^8 m^4 i 2 = 0. 02 × 0. 183 12 = 9. 72 × 10 −^6 ...

FIRST AND SECOND MOMENT OF AREAS 99 where A=( 8. 0 )( 3. 0 )=24 cm^2 and H= 12 .5cm Hence IXX= 18 + 24 ( 12. 5 )^2 =3768 cm^4 Fo ...

100 MECHANICAL ENGINEERING PRINCIPLES Figure 7.35 [18636 mm^4 ] 20 30 Figure 7.35 Figure 7.36 [10443 mm^4 ] 20 30 Figure 7.3 ...

FIRST AND SECOND MOMENT OF AREAS 101 (a) 16 cm^4 (b) 4 cm^4 (c) 36 cm^4 (d) 144 cm^4 G 60 mm 15 mm 20 mmG X X Figure 7.41 The s ...

102 MECHANICAL ENGINEERING PRINCIPLES Assignment 2 This assignment covers the material contained in Chapters 5 to 7. The marks f ...

8 Bending of beams At the end of this chapter you should be able to: define neutral layer define the neutral axis of a beam’s c ...

104 MECHANICAL ENGINEERING PRINCIPLES Hence, extension ofAB =δ=(R+y)θ−Rθ=yθ Now, strainε=extension/original length, i.e. ε= yθ R ...

BENDING OF BEAMS 105 But from equation (8.5), σ=E y R Therefore, ∫y 1 −y 2 Ey R bdy= 0 Now,EandRare constants, hence E R ∫y 1 −y ...

106 MECHANICAL ENGINEERING PRINCIPLES The total weight on the beam=wL,andasthe beam is symmetrically loaded, the values of the e ...

BENDING OF BEAMS 107 The maximum stress occurs at the outermost fibre of the beam’s cross-section fromNA,namelyatyˆ. By inspecti ...

108 MECHANICAL ENGINEERING PRINCIPLES as shown in Figure 8.11, determine the maximum stress in the beam. [34 MPa] 40 mm Thicknes ...

9 Torque At the end of this chapter you should be able to: define a couple define a torque and state its unit calculate torque ...

110 MECHANICAL ENGINEERING PRINCIPLES Problem 3. The circular hand-wheel of a valve of diameter 500 mm has a couple applied to i ...

TORQUE 111 Power P= 2 πnT(from above),from which, torque, T= P 2 πn Nm where power,P = 2 .50 kW=2500 W and speed, n= 1000 /60 re ...