ppt of subject S.A.-2 of civil engineering

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