TEMPERATURE EFFECT Due to temperature changes , development of a horizontal

thrust in arch without loading is known as temperature effect.

Derivation

Let α =co-efficient of thermal expansion of the arch

material

L=arch of span.

T= change of temperature in ˚C.

So Thermal expansion = αLT

Solving for H we get

For Circular ArchHorizontal thrust at support

Maximum bending moment= H x R.

For Parabolic ArchHorizontal thrust at support

Maximum bending moment= H x h.

Rib Shortening As a result of the axial thrust in the arch , the arch tends to

become deeper and hence as a consequence the horizontal

thrust tends to reduce.

DerivationAxial thrust N=Vsinθ + Hcosθ .

Moment at any section y distance apart in y axis

Mx= M-Hy

So by castigliano’s theorem

So,

Solving we get

has minimum value at crown.

Am= mean value of

Since

So that

Effect of V in rib shortening is negligible.

So ,

Combined Effect Of Temperature And

Rib Shortening Effect We get the expression

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