What is the pressure the hoop exerts on the cylinder

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Unformatted text preview: 0 N 4 z y yy Normal Stress: yA AA A Axial Stress 5 mm 5 mm z at all points: x z B BB 5 mm B 5 mm y A x B x z B 5 mm x x y y Total Normal Stress: A A zB B 5 mm 5 mm 5 mm y A 5 mm Flexural Stress : y A y B A z B 5 mm 5 mm 5 mm 5 mm x y A B 5 mm 5 mm B 5 mm y 0.4 m A 13- 36,37) Hibbeler, 4th ed 0 N·m 0.125 m y 150 N z 3 z 4 5 mm z B Torsional Shear Stress: y A y A y A 5 mm z x B B 5 mm 5 mm y A y A 5 mm 5 mm x B 5 mm y 150 Nmm 5 z 3 4 x B 5 mm 13- 36,37) Hibbeler, 4th ed y A y A y A Transverse Shear Stress: x zy B A B y A 5 mm 5 mm x y y A A z z B 5 mm 5 mm B 5 mm 5 mm B x z x B 5 mm 5 mm B 5 mm y 13- 36,37) Hibbeler, 4th ed y Total Shear Stress: z 400 mm a 20 N · m x a 125 mm x y A z 5 mm B Section a–a Volume Elements: Point A: y z x y Point B: z x 3 5 4 150 N Thin- Walled Pressure Vessels •  Consider a cylindrical vessel of internal radius r, wall thickness t and internal pressure p: •  Stress in the circumferenRal direcRon is σh and is called the hoop stress. Your book calls this σ1. •  Stress in the longitudinal direcRon is σh. Your book calls this σ2. •  Radial stress is small compared with hoop and longitudinal. •  Stress in any direcRon of a spherical vessel: 13- 13) Hibbeler, 4th ed 24 in. An A- 36 steel hoop has an inner diameter of 23.99 in., thickness of 0.25 in., and width of 1 in. If it and the 24-in.- diameter rigid cylinder have a temperature of 65° F, determine the temperature to which the hoop should be heated in order for it to just slip over the cylinder. What is the pressure the hoop exerts on the cylinder, and the tensile stress in the ring when it cools back down to 65° F? Given: for hoop Find: T2, temperature when hoop just fits (d2 = 24in), stress in hoop at T1 (room temp) 13- 13) Hibbeler, 4th ed To find T2: Cooling back to T1 : Pressure on cylinder : 24 in. M Ay x M M B DeflecRon of Beams CBy V P1 V A •  The displacement υ at each A point of the longitudinal axis of a M M beam is called the elas(c curve. •  υ is concave up when M > 0 and concave down when M < 0. M M PosiRve Bending M M M M B P1 P2 D V C E P2 V E D V MM V MM NegaRve Bending M •  M has inflecRon points where M υ = 0. •  At supports υ or dυ/dx may be zero. υA = υD = 0 Inflection Pt. Beam DeflecRon •  Calculate deflecRon by integraRng M(x) twice: •  We assumed that EI is constant with respect to x. •  Recall: Then: •  And: Then: Beam DeflecRon Process •  Find support reacRons first with FBD of enRre beam. •  Construct the load w or moment M expressions in terms of the disconRnuity funcRons. •  If you constructed w, integrate t...
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