Procedure of Initial Sizing Design Criteria Initial Sizing Design Criteria – Upper Skin Panel No local buckling up to ultimate load They shall be sized using compression and shear interaction criteria: σ c τ s2 + ≤ 1.0 σ cr τ cr σ c = applied compression stress σ all = allowable compression stress of the panel, which is the smallest value of : crippling stress  skin local buckling stress  intermediate (Johnson Euler) column buckling stress τ s = applied shear stress τ all = allowable shear stress of the panel, which is the smallest value of :  skin shear local buckling stress  allowable shear stress of the material used Design Criteria – Lower Skin Panel shall be sized using tension and shear interaction criteria: σ all ≥ 1.0 σ comb where as material failure according to Von Mises : σ comb = σ t + 3τ σ all σt τs = allowable tension stress of the material used = applied tension stress = applied shear stress Please note that Lower panel is also critical due to fatigue The criteria have to be considered is : σ all −1G − ≥ 0.0 σt Design Criteria – Spars They shall be sized using shear criteria : τs τ all ≥ 1.0 τ s shear stress = applied τ all = allowable shear stress of the panel, which is the smallest value of:   skin shear local buckling stress allowable shear stress of the material used Design Criteria – Ribs Due to concentrated loads (attachments: engine, flaps, etc): Due to shear loads : Due to aerodynamic loads, the ribs shall be designed as beams simply supported at the spars The web shall be sized using shear criteria : τ s = applied shear stress τ all ≥ τs τ all = allowable shear stress of the panel, which is the smallest value of:   skin shear local buckling stress allowable shear stress of the material used Design Criteria – Ribs Cont Due to crushing loads : The stiffener shall be sized using compression criteria : σ all ≥ 1.0 σ σ all = allowable compression stress of the panel, which is the smallest value of :  Column buckling stress  Allowable compression stress of the material σ = applied compression stress Initial Sizing: Upper and Lower Skin Panel i ii iii iv At various points across the span evaluate the idealised depth of the primary structural box, h Calculate the effective direct loads, P, in the top and bottom surfaces required to react the appropriate bending moment, M, at each section from: P = M/h Evaluate the allowable stress, fb Evaluate the cross section area required, Ab by dividing the load P by the allowable stress fb Initial Sizing: Upper and Lower Skin Panel Initial Sizing: Upper and Lower Skin Panel  For a mass boom design, where all the bending moment is reached only by the spar caps: P M Ab = = f b hf b  Initially assume Ab is divided equally between all the boom spar caps on one side of the box, and fb is the allowable proof stress in this case Initial Sizing: Upper and Lower Skin Panel  For a distributed flange assume initially a uniform effective thickness across the width, w, to give M te = hwf b  Typically this thickness will be made up of skin and stringer area The effective stringer are being about half of that of the skin area Thus the actual skin thickness is about: 0.65M te = hwf b Allowable Stresses - Direct (bending) Stress   The accurate evaluation of the allowable bending stress is complex, requiring a knowledge of the detail features of the structure both in the compression and tension surfaces Experience suggests that if the magnitude of the allowable compression stress is also used for the tension surface it makes the right order of allowance for fatigue/crack propagation requirements although this assumption can only be approximate, especially when the allowable compression stress approaches the 0.2% proof value Thus the same allowable stress level may be initially assumed in both surfaces The main parameter in determining the allowable compression stress is the loading intensity If mass booms are used as the primary means of reacting direct load, then it is appropriate to assume that under ultimate bending loads the 0.2% proof stress may be used Allowable Stresses - Direct (bending) Stress  When the concept is based on a distributed flange construction the allowable bending stress at ultimate loading may be assumed to be the lesser of the 0.2% proof stress or f b, where fb may be approximately represented by: 1/  P  f b = A FB    wL  where L is the local rib or frame spacing w is the width of the box perpendicular to the bending axis P is the effective end load A is a function of the material FB is dependant upon the form of construction   Note that the value of A are appropriate to allowable stress and (P/wL) in MN/m2 units In general the values of A give conservative values for Fb at stresses below the limiting value Typical values for FB are also given Initial Sizing: Spar Webs i Due to Overall Torsion Moment:   Estimate the enclosed area, A, of the primary structural box at representative sections across the span The corresponding shear flow is: QT = T/2A    Where T is now the applied distributed torsion, and QT will be nose up or nose down and hence positive or negative depending on the sign convention Select the allowable shear stress, fs as appropriate The mean material thickness needed to react the torsion moment is then: tq = T / 2Afs Initial Sizing: Spar Webs ii Combined with vertical shear loads  The shear flow in the webs due to the shear force is then: Qv = V/hT, where V is the applied vertical shear force  The net shear flow in the web is then approximately given by: x Qw = QV + QT w  Where x is the chordwise location of particular web relative to the mid point of the box The web thickness is then: Qw tw = fs Initial Sizing: Ribs Web i Due to concentrated loads (attachments: engine, flaps, etc): can be taken as a cantilever beam loaded by a vertical shear force equal to the hinge reaction and a bending couple due to the offset of the hinge chordwise from the rear spar location The spar web will react most of the vertical shear, and in practice if the hinge fitting is perpendicular to the rear spar, the rib flanges at the spar will be loaded by direct forces given by: x R = ±V h Where V is the hinge reaction x is the offset of the hinge from the spar h is the depth of the rib at the spar Initial Sizing: Ribs Web ii Due to shear loads : R = Q z1 − Q z Initial Sizing: Ribs Web Due to crushing loads : iii σn = Where: σn 2.σ t panel L E.h.trib = crushing stress at rib ; L = rib distance σupper = normal stress at upper panel ; H = rib height σlower = normal stress at lower panel ; trib = rib web thickness σ= abs (σ upperpanel ) + abs (σ lowerpanel )