Curved Beam - VTU e-Learning

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Distance of neutral axis to inner radius ci = rn - ri Distance of neutral axis to outer radius co = ro - rn = 153.045-125 = 28.045mm = 185-153.045 = 31.955mm Distance from centroidal axis to force l = rc -25 = 155-25 = 130mm Area of cross section A = bh = 30x60 = 1800mm 2 Bending moment about centroidal axis Mb = Fl = Fx130 Direct stress σd = = Bending stress at the inner fiber σbi = = 130F + Combined stress at the inner fiber σri = σd + σbi i.e., 75 = . + . F = 8480.4N =Capacity of the hook.
Problem no.12 Design of steel crane hook to have a capacity of 100kN. Assume factor of safety (FS) = 2 and trapezoidal section. Data: Load capacity F = 100kN = 10 5 N; Trapezoidal section; FS = 2 Solution: Approximately 1kgf = 10N ∴ 10 5 = 10,000 kgf =10t Selection the standard crane hook dimensions from table 25.3 when safe load =10t and steel (MS) ∴ c =11933; Z = 14mm; M = 71mm and h = 111mm bi= M = 7133 bo = 2xZ = 2x14 = 28 mm r1 = = = 59.5mm h = 111mm b o Z H M = b i CA NA h = 111 mm c 2 c o e c 1 b =28 o b =71 i c i r =59.5 mm i r n r = c r o l C L F
Page 1 and 2: CURVED BEAMS CONTENT: WHAT’S A C
Page 3 and 4: G1H1 = (R+Y) Ѳ Also Stress OR dF =
Page 5 and 6: Stresses in Curved Beam Consider a
Page 7 and 8: We know, stress σ = E.e We know, s
Page 9 and 10: ∴ M = b θ A.e ..... (iii) θ Fro
Page 11 and 12: 2 3 Neutral axis and centroidal axi
Page 14 and 15: Why stress concentration occur at i
Page 16 and 17: For a straight beam: Inner most fib
Page 18: e = rc - rn = 100 - 91.024 = 8.976m
Page 21 and 22: = i.e., 4674.069+83.61t +83.61t = 4
Page 23 and 24: σri = σd + σbi = 7.0736 105.00
Page 25 and 26: Bending stress at the outer fiber
Page 27 and 28: =150.34mm To find the centroidal ax
Page 29 and 30: Distance of neutral axis to inner r
Page 31 and 32: Problem no.7 Determine the maximum
Page 33 and 34: Maximum shear stress max = 0.5x σm
Page 35 and 36: ∴ Radius of centroidal axis rc =
Page 37 and 38: Combined stress =-198.189 N/mm σ r
Page 39 and 40: x = = 101.785mm Radius of
Page 41 and 42: Problem no.10 Compute the combined
Page 43 and 44: Bending stress at the inner fiber
Page 45 and 46: C2 = = 50mm c1 = 90-50= 40mm Mome
Page 47: Problem no.11 The section of a cran
Page 51 and 52: Applied force F = 10 5 N Area of cr
Page 53 and 54: Problem no.13 The figure shows a lo
Page 55 and 56: Draw the critical section at PP-Q a
Page 57 and 58: 25 ro = 75 + 2 = 87.5 mm A = π 4 d
Page 59 and 60: The ring is symmetrical and is load
Page 61 and 62: As this quantity is positive the di
Page 63 and 64: The stress at inner (σ1Ai) ) and o
Page 65 and 66: As per Castigliano’s theorem \
Page 67 and 68: The stress at any angle Ѳ can be f
Page 69 and 70: Distance of neutral axis to outer r
Page 71 and 72: Problem 16 Determine the stress ind
Page 73 and 74: Consider the cross section B - B At
Page 75 and 76: Distance of neutral axis to outer r
Page 77 and 78: Using usual notations prove that th
Page 79 and 80: Substituting the value of the σx f
Page 81 and 82: 1 ∆ = 1 {From equation (x
Page 83 and 84: VTU,Jan/Feb.2005 Fig.1.35 5. Determ
Page 85: REFERENCE BOOKS • “MECHANICAL E

Curved Beam - VTU e-Learning

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