The document discusses temperature effects and rib shortening effects in arches. Due to temperature changes, arches develop a horizontal thrust without any loading, known as the temperature effect. For circular arches, the horizontal thrust at supports creates a maximum bending moment equal to the thrust multiplied by the radius. For parabolic arches, the maximum bending moment equals the horizontal thrust multiplied by the height. Rib shortening occurs as the arch tries to become deeper under axial thrust, reducing the horizontal thrust. The combined effects of temperature and rib shortening on an arch can be expressed through equations that calculate the net horizontal thrust.

2. TEMPERATURE EFFECT
 Due to temperature changes , development of a horizontal
thrust in arch without loading is known as temperature effect.

3. 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

4. Solving for H we get

5. For Circular Arch
Horizontal thrust at support
Maximum bending moment= H x R.

6. For Parabolic Arch
Horizontal thrust at support
Maximum bending moment= H x h.

7. 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.

8. Derivation
Axial thrust N=Vsinθ + Hcosθ .
Moment at any section y distance apart in y axis
Mx= M-Hy
So by castigliano’s theorem
So,

9. Solving we get
has minimum value at crown.
Am= mean value of
Since

10. So that
Effect of V in rib shortening is negligible.
So ,

11. Combined Effect Of Temperature And
Rib Shortening Effect
 We get the expression

12. THANK YOU