Curved Beam - VTU e-Learning

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Problem no.6 Determine the stresses at point A and B of the split ring shown in fig.1.9a Solution: Redraw the critical section as shown in the figure. Radius of centroidal axis rc = 80mm Inner radius of curved beam ri = 80 Outer radius of curved beam ro = 80 + Radius of neutral axis rn = = √√ = 50mm = 110mm =77.081mm Applied force F = 20kN = 20,000N (compressive) Area of cross section A = π d2 = π x602 = 2827.433mm 2 Distance from centroidal axis to force l = rc = 80mm Bending moment about centroidal axis Mb = FI = 20,000x80 =16x10 5 N-mm Distance of neutral axis to centroidal axis e = rc rn = 80 77.081 =2.919mm
Distance of neutral axis to inner radius ci = rn ri = 77.081 50 = 27.081mm Distance of neutral axis to outer radius co = ro rn = 110 77.081 = 32.919mm Direct stress σd = = . = 7.0736N/mm 2 (comp.) Bending stress at the inner fiber σbi = Bending stress at the outer fiber σbo = Combined stress at the inner fiber σri = σd + σbi = 7.0736 105.00 = . .. = 105N/mm 2 (compressive) = . .. = 58.016N/mm 2 (tensile) = 112.0736N/mm 2 (compressive) Combined stress at the outer fiber σro = σd + σb = 7.0736+58.016 Maximum shear stress = 50.9424N/mm 2 (tensile) max = 0.5x σmax = 0.5x112.0736 = 56.0368N/mm 2 , at B
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: =150.34mm To find the centroidal ax
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 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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Curved Beam - VTU e-Learning

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