HW#4 - AAE 352 S08 HW #4 Solutions 2.5 Mechanics of...

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Mechanics of Aircraft structures C.T. Sun 2.5 A cantilever beam of a rectangular cross-section is subjected to a shear force V as shown in Fig. 2.17. The bending stress is given by I Mz xx = σ where ) ( x L V M = . Assume a state of plane stress parallel to the x-z plane, i.e., 0 = = = yz xy yy τ . Find the transverse shear stress ( ) zx xz = by integrating the equilibrium equations over the beam thickness and applying the boundary conditions 0 = xz at 2 h z ± = . Hint: From the equilibrium equation 0 = + z x xz xx we have x M I z x z xx xz = = Figure 2.17 Cantilever beam subjected to a shear force Solution: (a) Bending moment is ) ( x L V M = , so V x M = (b) From the equilibrium equation for a state of plane stress parallel to the x-z plane, we have z I V x M I z x z xx xz = = = Therefore, + = = C z I V dz z I V xz 2 2 2.5.1 AAE 352 S08 HW #4 Solutions
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Mechanics of Aircraft structures C.T. Sun (c) Applying the B.C.: 0 = xz τ at 2 h z ± = we have 0 2 2 2 = + C h I V => I Vh C 8 2 = So ( 2 2 2 4 8 2 z h ) I V C z I V xz = + = a l s o 12 3 bh I = => () ( ) 2 2 3 2 2 4 2 3 4 8 z h bh V z h I V xz = = --- ANS 2.5.2
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Mechanics of Aircraft structures C.T. Sun
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This note was uploaded on 04/11/2008 for the course AAE 352 taught by Professor Chen during the Spring '08 term at Purdue.

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HW#4 - AAE 352 S08 HW #4 Solutions 2.5 Mechanics of...

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