Page 64 - Aircraft Stuctures for Engineering Student

Problems 49

compressive, 3p, parallel to Ox,
tensile, 2p, parallel to Oy,
shearing, 4p, in planes parallel to Ox and Oy
in a sense tending to decrease the angle xOy
Determine the direction in which a certain point on the plate will be displaced; the
coordinates of the point are (2,3) before straining. Poisson~s ratio is 0.25.

Am. 19.73" to Ox
P.2.2 What do you understand by an Airy stress function in two dimensions? A
beam of length 1, with a thin rectangular cross-section, is built-in at the end x = 0 and
loaded at the tip by a vertical force P (Fig. P.2.2). Show that the stress distribution, as
calculated by simple beam theory, can be represented by the expression
q5 = Ay3 + By3x + C~X

as an Airy stress function and determine the coefficients A, B, C.

Ans. A = 2Pl/td3, B = -2P/td3, C = 3P/2td

YI

Fig. P.2.2

P.2.3 A thin rectangular plate of unit thickness (Fig. P.2.3) is loaded along
the edge y = +d by a linearly varying distributed load of intensity MJ =px with

Fig. P.2.3