Page 48 - Aircraft Stuctures for Engineering Student

Problems 33

Am. or = 100.2N/mm2, 0 = 24" 11'

a11 = -20.2 N/IIUII~, 6' = 114" 11'
T,,, = 60.2N/mm2, at 45" to principal planes
P.1.2 At a point in an elastic material there are two mutually perpendicular
planes, one of which carries a direct tensile stress at 50N/mm2 and a shear stress
of 40N/mm2, while the other plane is subjected to a direct compressive stress of
35 N/mm2 and a complementary shear stress of 40 N/mm2. Determine the principal
stresses at the point, the position of the planes on which they act and the position
of the planes on which there is no normal stress.
e
ar = ~~.~N/IIuII~, 210 38'
=
aII = -50.9N/mm2; 0 = 111" 38'
No normal stress on planes at 70" 21' and -27" 5' to vertical.
P.1.3 Listed below are varying combinations of stresses acting at a point and
referred to axes x and y in an elastic material. Using Mohr's circle of stress determine
the principal stresses at the point and their directions for each combination.
a, N/m2 ay N/m2 7.u N/m2
(i) +54 +30 +5
(ii) +30 +54 -5
(iii) -60 -36 +5
(iv) +30 -50 +30

Am. (i) aI = +55N/mm2, arI = +29N/mm2, a1 at 11.5" to x axis.
(ii) or = +55 N/mm2, aII = +29 N/mm2, aII at 11 .5" to x axis.
(iii) or = -34.5N/mm2; arI = -61 N/mm2, aI at 79.5" to x axis.

(iv) aI = +40N/mm2, aII = -60N/mm2, aI at 18.5" to x axis.
P.1.4 The state of stress at a point is caused by three separate actions, each of
which produces a pure, unidirectional tension of 10N/mm2 individually but in
three different directions as shown in Fig. P.1.4. By transforming the individual

IO N/rnrn2

IO N/mrn2 IO N/rnm2

IO N /mm2 IO N/rnrnz

IO N/mrn2
Fig. P.1.4