Analysis of Arches & Cables Notes | EduRev

Structural Analysis

GATE : Analysis of Arches & Cables Notes | EduRev

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Arches

Three Hinged Arches

  1. Three Hinged Parabolic Arch of Span L and rise 'h' carrying a UDL over the whole span
    Ds = 0
    BMc = 0
    H = wl2/8h
    Mx = VAx - wx2/2 - HyAnalysis of Arches & Cables Notes | EduRev where, H = Horizontal thrust
    VA = Vertical reaction at A = wl/2
    Analysis of Arches & Cables Notes | EduRevSimply supported beam moment i.e., moment caused by vertical reactions.
    Hy = H-moment
    DS = Degree of static indeterminacy
    BMC = Bending Moment at C.
  2. Three Hinged Semicircular Arch of Radius R carrying a UDL over the whole span.Analysis of Arches & Cables Notes | EduRevH = wR/2
    Mx = -wR2/2 [sin θ - sin2 θ]Analysis of Arches & Cables Notes | EduRevMmax = -wR2/8
    BMc = 0
    Point of contraflexure = 0
  3. Three Hinged Parabolic Arch Having Abutments at Different Levels
    (i) When it is subjected to UDL over whole spanAnalysis of Arches & Cables Notes | EduRevAnalysis of Arches & Cables Notes | EduRev
    (ii) When it is subjected to concentrated load W at crown
    Analysis of Arches & Cables Notes | EduRevAnalysis of Arches & Cables Notes | EduRev
  4. Three Hinged Semicircular Arch Carrying Concentrated Load W at CrownAnalysis of Arches & Cables Notes | EduRevH = VA = VB = W/2

Temperature Effect on Three Hinged Arches

Analysis of Arches & Cables Notes | EduRev

  1. Analysis of Arches & Cables Notes | EduRevWhere, Δh = free rise in crown height
    l = length of arch
    h = rise of arch
    α = coefficient of thermal expansion
    T = rise in temperature in 0C
  2. H α 1/h
    Where, H = horizontal thrust
    and h = rise of arch
  3. % Decrease in horizontal thrust = δh/h x 100

Two Hinged Arches

Analysis of Arches & Cables Notes | EduRevTwo hinged arch of any shape

Analysis of Arches & Cables Notes | EduRev
DS = 1
Where, M = Simply support Beam moment caused by vertical force.

  1. Two hinged semicircular arch of radius R carrying a concentrated load 'w' at the town.
    H = w/π
    Analysis of Arches & Cables Notes | EduRevTwo Hinged Circular arch
  2. Two hinged semicircular arch of radius R carrying a load w at a section, the radius vector corresponding to which makes an angle α with the horizontal.Analysis of Arches & Cables Notes | EduRevTwo Hinged Circular archH = w/π sin2 α
  3. A two hinged semicircular arch of radius R carrying a UDL w per unit length over the whole span.
    Analysis of Arches & Cables Notes | EduRev
    Two Hinged Semicircular arch
  4. A two hinged semicircular arch of radius R carrying a distributed load uniformly varying from zero at the left end to w per unit run at the right end.
    Analysis of Arches & Cables Notes | EduRevTwo Hinged Semicircular archH = 2/3.wR/π
  5. A two hinged parabolic arch carries a UDL of w per unit run on entire span. If the span off the arch is L and its rise is h.
    Analysis of Arches & Cables Notes | EduRev
    Two Hinged parabolic arch
    H = wl2/8h
  6. When half of the parabolic arch is loaded by UDL, then the horizontal reaction at support is given by
    Analysis of Arches & Cables Notes | EduRev
    Two Hinged parabolic arch
  7. When two hinged parabolic arch carries varying UDL, from zero to w the horizontal thrust is given by
    Analysis of Arches & Cables Notes | EduRev
    Two Hinged parabolic arch
    H = wl2/16h
  8. A two hinged parabolic arch of span l and rise h carries a concentrated load w at the crown.
    H = 25 wl/ 128 h

Analysis of Arches & Cables Notes | EduRev

Two Hinged parabolic arch
Temperature Effect on Two Hinged Arches

Analysis of Arches & Cables Notes | EduRev

Analysis of Arches & Cables Notes | EduRev

  1. Analysis of Arches & Cables Notes | EduRev
    where H = Horizontal thrust for two hinged semicircular arch due to rise in temperature by T 0C.
  2. Analysis of Arches & Cables Notes | EduRev
    where l0 = Moment of inertia of the arch at crown.
    H = Horizontal thrust for two hinged parabolic arch due to rise in temperature T 0C.

Reaction Locus for a Two Hinged Arch

  1. Two Hinged Semicircular Arch
    Reaction locus is straight line parallel to the line joining abutments and height at πR/2
    Analysis of Arches & Cables Notes | EduRev
  2. Two Hinged Parabolic Arch
    Analysis of Arches & Cables Notes | EduRev

Analysis of Arches & Cables Notes | EduRev

Eddy's Theorem

Mxαy

Analysis of Arches & Cables Notes | EduRevwhere, MX = BM at any section
y = distance between given arch linear arch

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