1:31 PM Tue Jan 30 7 4281 HW 3 Sp24.pdf Plate Buckling = 1. (20 pts pts) Consider shear panels with uniform thickness of 5 mm made of aluminum alloy with E 70GPa, and v = = 0.33. Assume simply supported boundary conditions on all edges. One panel is flat while the other panel comprises the same amount of material but is bent into a cylindrical shape. a) If the panels are loaded with uniform shear along their edges, determine the buckling stress Ter for each of the two panels. Use the charts included on the last page of this assignment for the curved panel case. Include marked copies of these charts illustrating your solution. (Note: Megson Fig. 9.3(a) does not apply to shear loading.) b) If the panels are loaded with uniform normal stress along the shorter end, as shown, determine the buckling stress er for each of the two panels. Also, for the case of the flat panel, make a sketch illustrating the buckling mode that you expect. [Note: for the curved panel case, look up an appropriate formula/data from "Roark's Formulas for Stress and Strain. Available at the library, or full text through the library web page. https://www-accessengineeringlibrary- com.portal.lib.fit.edu/content/book/9781260453751 ] c) Compare all results and comment (by 'comment,' I mean analyze the results and try to say something interesting about them. Do not simply restate the steps followed in words, nor simply report the numerical results in words). 0.5 m Part a SS SHEAR LOAD SS Ss SS SS SS SS SS Part b SS SS $$ SS AXIAL LOAD SS SS FLAT SS 1.5 m CYLINDRICAL 55 SS 0.5 m SS Continued on next page SS 1 m SS 1.5 m 2. (20 pts) Stiffened Shear Web and Diagonal Tension Beam. Consider a simple stiffened web beam as shown in the figure. The beam is cantilevered at one end, and supports a design tip load of 30 kN (this includes factors of safety) at the other end. Let us begin to design this beam using some simple idealizations This will give us an approximate 146 Dashboard 000 Calendar To Do Notifications 33% Inbox 1:31 PM Tue Jan 30 7 4281 HW 3 Sp24.pdf 2. (20 pts) Stiffened Shear Web and Diagonal Tension Beam. Consider a simple stiffened web beam as shown in the figure. The beam is cantilevered at one end, and supports a design tip load of 30 kN (this includes factors of safety) at the other end. Let us begin to design this beam using some simple idealizations. This will give us an approximate idea of the required dimensions of the parts comprising the beam, though refinement to the calculations would be necessary for more exact answers. Consider this exercise as a first step. Assume all parts are made of Aluminum 2024-T4 with stiffness E = 73 GPa, Poisson's ratio v= 0.33, and an ultimate tensile strength = 470 MPa, and Tult = 280 MPa. a) Longitudinal Stiffeners, Idealized Case Using the idealization that the web carries no axial load, and assuming that the longitudinal stiffeners are uniform along their entire length from tip to root, determine the minimum cross-sectional area Af required for the lower longitudinal stiffener based on tensile strength. b) Strength-based web thickness computation Suppose you attempt to size the web thickness by setting = Tult. What minimum web thickness is required by this analysis? Note that we do not expect this to be a valid analysis. Explain why. Web c) Non-buckling web Assuming that the thickness of the web is controlled by shear buckling of the panels, what minimum panel thickness is required to prevent buckling of the panels up to the design load. This requires an equation describing the buckling response of a rectangular panel under pure shear as shown in sketch at right. Assume simply-supported boundary conditions on the edges of the panel. d) Complete diagonal tension As discussed in Megson Section 9.7, a more efficient design can be made by permitting the web to buckle under loading. The extreme case of this is a "Complete Diagonal Tension" beam, in which case the web is assumed to support only tensile forces along one diagonal, and zero force along the other. Section 9.7.1 of Megson discusses the analysis of such a beam (though without specifically addressing the web thickness). Based on the analysis in Megson, determine the required web thickness for this case. Assume = 45. Assume that failure is governed by the tensile stress in the web. Compare your results for parts b, c, and d and comment. e) Longitudinal Stiffeners, Complete diagonal tension case As discussed in 9.7.1, in the complete diagonal tension case, the loads in the stiffeners are not the same as using the simple idealization in a. Compute the axial loads carried in each longitudinal stiffener at the wall for this case, and compare with the results using the idealization in part a. 30KNI 2 m web web web web web web m (typical) 3m 33% 146 Dashboard Calendar To Do Notifications Inbox 1000 1:31 PM Tue Jan 30 7 ... 4281 HW 3 Sp24.pdf 3. V-M Diagram Review (20 pts) Consider the aircraft shown in the figure. Given the following: The gross weight is 150,000 lb, with a center of gravity at BS 250 Note that "Body Station" (BS) refers to the longitudinal position of cross-sections relative to a reference point (BS 0), measured here in inches. Given: Neglecting aerodynamic moments, in steady level flight, Lw = 128,571 lb and LT = 21,429 lb. Consider the fuselage of this aircraft as a beam, and find its internal resultants (V,M) for the steady-level flight condition. Assume that the weight of the fuselage and its contents produce a uniform distributed load of 150 lb/in over the entire 600 inch length. Do not turn this distributed load into an equivalent point force. Treat the weight of the wings and its contents as a point force of 58,000 pounds acting at BS 162 Given: the empennage (tail) has a total weight of 2000 lb, and is treated as a point load acting at BS 560. a) Sketch V-M diagrams for the fuselage in this case. Include numerical values of V and M at key points, such as locations of discontinuities, locations of min and max, etc (i.e. there should be enough information that the V-M diagrams are completely defined quantitatively). Justify numerical values. b) Based on the V-M diagram, make an exaggerated, qualitative sketch showing the deformation of the fuselage. (Recall, the relationship between moment and curvature) Lw LTA B.S. O 200 550 600 33% 146 Dashboard Calendar To Do Notifications Inbox 1000 33% 1000 Data for problem 1. Submit a marked-up copy of these graphs with your solution. 1:31 PM Tue Jan 30 > < 4281 HW 3 Sp24.pdf 100 C 10 OnQo 8 10 15 2.0. 3.0 - 12M 10 Ter a E Ter C 12(1 - v) Az rt ( 1000 CID 100 1.0. 1.5. C 10 Figure 12.10.5 Theoretical shear buckling coefficient for long, simply- supported curved panels Figure 12.10.6 t 2.0- Cylinder, Tcr C z (7) 12 - 1321 TE Zb b ri V1 1 100 1000 1 10 100 1000 Zb b Theoretical shear buckling coefficient for short, simply- supported curved panels Dashboard 146 808 Calendar To Do Notifications Inbox