Chapter 7_Stringers and Shear Panels

Chapter 7_Stringers and Shear Panels - CHAPTER 7 STRINGERS...

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1 CHAPTER 7 STRINGERS AND SHEAR PANELS For semi-monocoque structures with stringers and shear panels, one can use a simplified model to determine the following: Axial stress on stringers Shear flows in the shear panels 7.1 Simplified Model with Stringers and Shear Panels Semi-monocoque structures: shells or skins that are reinforced with stiffeners and/or spars. Fuselage or wing can be considered semi-monocoque structures. To simplify the analysis, semi-monocoque structures can be idealized by introducing the following assumptions: 1. Stiffeners, stringers, longerons and flanges are assumed to carry only axial stress σ xx ; their cross-sections are modeled as concentrated areas. 2. Skin and web are assumed to carry only shear stress. z x y idealized model idealized model
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2 7.2 Axial Stress on the Stringers Consider a wing or fuselage section modeled with stringers and shear panels as shown below. The C-S is subjected to M x M x V x V x yz y z () , , () and Recall the following: Axial stress σ xx is related to axial strain ε xx as follows: 12 3 xx xx EE C C z C y ==+ + ( 1 ) Using the above expression, the resultant forces and moments can be expressed as follows: 3 xx xx F dA E dA E C C z C y dA σε == = + + ∫∫ 3 yx x x x M z d AE z d C C z C y z d A = + + (2) 3 zx x x x M yd A Ey d A E CC z C y y d A = + + For a section of single material, E is uniform over the section and equation (2) can be expressed as 3 FE Cd Cz d Cy d A =+ + 2 3 y M EC zdA EC z dA EC yzdA + ( 3 ) 2 3 z M EC ydA EC yzdA EC y dA + Stringer #1 #2 #3 #4 #5 #6 V z V y A 3 (,) 33 A y z n nn , : cross-sectional area of stringer #n : and coordinates of stringer #n
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3 For shear panels or skins, it is assumed that σ xx 0 . Accordingly, the integrations in equation (3) are carried out over the stringer areas only. The origin of the CB axes is then determined as follows: () () 1 () 1 nn n C n n y A ydA y AA = = == 1 1 n C n n zA zdA z = = ( 4 ) Note : Recall that y and z are the reference axes described in the previous chapter. Also, 2 2( ) ( ) 1 y n I zdA z A = ⎡⎤ ⎣⎦ 2 ) ( ) 1 z n I ydA y A = ( 5 ) () () () 1 nn n yz n I yzdA y z A = For the n-th stringer of a section of single material, 12 3 , ( 1 , 2 , , 6 ) n xx EC Cz Cy n =+ + = " (6) Axial stress n xx is assumed to be constant over the stringer cross-sectional area n A . For CB axes, EA F x u C x = = 0 1 ) ( ) ( 1 2 2 0 2 2 z yz y z yz z y M I M I I I I E x w C = = (7) ) ( ) ( 1 2 2 0 2 3 z y y yz yz z y M I M I I I I E x v C + = = Equations (6) and (7) can be used to determine the stringer axial stresses when the resultant force and moments are given over a cross-section.
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4 Example 1 : Consider a single-cell section shown below. Resultant moment 0 M M y = is acting over the rectangular section of a wing box with four stringers and four shear panels as shown below. The wing section is assumed uniform along the span of our interest. The stringer areas and the panel thickness are shown in the sketch.
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Chapter 7_Stringers and Shear Panels - CHAPTER 7 STRINGERS...

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