By T.H.G. Megson
Plane buildings for Engineering scholars is the prime self contained airplane constructions direction textual content. It covers all primary matters, together with elasticity, structural research, airworthiness and aeroelasticity. Now in its fourth variation, the writer has revised and up to date the textual content all through and extra new case research and labored instance fabric to make the textual content much more obtainable. features a strategies guide to be had to all adopting lecturers. * New association aids realizing of the basics of structural research and emphasizes purposes to aircraftstructures* New labored examples in the course of the textual content relief figuring out and relate thoughts to actual global purposes* extra assurance comprises digital paintings, stress box beams, submit buckling habit, fabric houses, composite buildings and crack propagation* an intensive plane layout undertaking case research exhibits the appliance of the most important ideas within the e-book* finish of bankruptcy routines and accompanying Instructor's guide at http://textbooks.elsevier.com
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Extra resources for Aircraft Structures for Engineering Students, Fourth Edition (Elsevier Aerospace Engineering)
13) is the negative reciprocal of Eq. 10) then the angles 2θ given by these two equations differ by 90◦ or, alternatively, the planes of maximum shear stress are inclined at 45◦ to the principal planes. 8 Mohr’s circle of stress The state of stress at a point in a deformable body may be determined graphically by Mohr’s circle of stress. 6 the direct and shear stresses on an inclined plane were shown to be given by σn = σx cos2 θ + σy sin2 θ + τxy sin 2θ (Eq. 8)) 17 18 Basic elasticity Fig. 12 (a) Stresses on a triangular element; (b) Mohr’s circle of stress for stress system shown in (a).
9). Note that the construction of Fig. 12(b) corresponds to the stress system of Fig. 12(a) so that any sign reversal must be allowed for. Also, the Oσ and Oτ axes must be constructed to the same scale or the equation of the circle is not represented. The maximum and minimum values of the direct stress, viz. the major and minor principal stresses σI and σII , occur when N (and Q ) coincide with B and A, respectively. Thus σ1 = OC + radius of circle = (σx + σy ) + 2 CP12 + P1 Q12 or σI = (σx + σy ) 1 2 + (σx − σy )2 + 4τxy 2 2 and in the same fashion σII = (σx + σy ) 1 2 − (σx − σy )2 + 4τxy 2 2 The principal planes are then given by 2θ = β(σI ) and 2θ = β + π(σII ).
18) It follows that εy = ∂y ⎪ ⎪ ⎪ ⎪ ∂w ⎪ ⎪ ⎭ εz = ∂z The shear strain at a point in a body is deﬁned as the change in the angle between two mutually perpendicular lines at the point. Therefore, if the shear strain in the xz plane is γxz then the angle between the displaced line elements O A and O C in Fig. 15 is π/2 − γxz radians. Now cos A O C = cos(π/2 − γxz ) = sin γxz and as γxz is small then cos A O C = γxz . 19) 23 24 Basic elasticity We have previously shown, in Eq. 17), that O A = δx 1 + ∂u ∂x O C = δz 1 + ∂w ∂z Similarly But for small displacements the derivatives of u, v and w are small compared with l, so that, as we are concerned here with actual length rather than change in length, we may use the approximations O A ≈ δx O C ≈ δz Again to a ﬁrst approximation (A C )2 = δz − ∂w δx ∂x 2 + δx − ∂u δz ∂z 2 Substituting for O A , O C and A C in Eq.