Curved Beam - VTU e-Learning

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Distance of neutral axis to inner radius ci = rn - ri = 136.1038-100 = 36.1038mm Distance of neutral axis to outer radius co = ro - rn = 180-136.1038 = 43.8962mm Distance from centroidal axis to force Applied force F = 9000N l = 175+ rc = 175+140 = 315mm Area of cross section A = 50x80 = 4000mm 2 Bending moment about centroidal axis Mb = FI = 9000x315 Direct stress σd = = 2835000 N-mm = = 2.25N/mm2 (tensile) Bending stress at the inner fiber σbi = Bending stress at the outer fiber σbo = = . . = 65.676N/mm 2 (tensile) = . . = 44.326N/mm 2 (compressive) Combined stress at the inner fiber σri = σd + σbi = 2.25+65.676 = 67.926N/mm 2 (tensile) Combined stress at the outer fiber σro = σd + σbo = 2.25 44.362 = 42.112 N/mm 2 (compressive)
Maximum shear stress max = 0.5x σmax = 0.5x67.926 = 33.963 N/mm 2 , at the inner fiber The stress distribution on the critical section is as shown in the figure. Combined stress = -42.112 N/mm σ ro 2 Bending stress σbo=-44.362 N/mm Direct stress ( σd) 2 CA NA h =80 mm σ ri=67.926 N/mm 2 σ bi=65.676 N/mm 2 σ d=2.25 N/mm 2 b = 50 mm
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: Problem no.7 Determine the maximum
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 and 48: Problem no.11 The section of a cran
Page 49 and 50: Problem no.12 Design of steel crane
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
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