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5 Two-Dimensional Problems in Cartesian Co-ordinate System
Fig. 5.15 Variation of shear stress τ xy
Thus, τ xy varies parabolically with z. However, it is independent of x; i.e. its
value is the same for all values of x (Fig. 5.15).
∴ At y = 0, τ xy = −
3
4
F
h
At y = ±h, τ xy =
3
4
F
h 3 (h)
2
−
3
4
F
h
= 0
5.10 Exercises
1. Write short notes on the following.
(i) Plane stress and plain-strain problems.
(ii) Airy’s stress function
2. Explain the use of polynomials in the solution of structural problems.
3. Determine the stress fields that arise from the following stress functions
(a) φ = cy
2 (b) φ = Ax
2
+ Bx y + Cy
2 (c) φ = Ax
3
+ Bx
2 y + C x y
2
+ Dy
3
4. Investigate what problem of plane stress is solved by the following stress
function.
φ =
F
d 3 x y
2
(3d − 2y)
5. Discuss what problems of plane stress can be solved using at a 4th degree
polynomial.