1. (15 pts) An idealized box beam structure has a single-cell, closed cross-section, square shape. There...

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1. (15 pts) An idealized box beam structure has a single-cell, closed cross-section, square shape. There are four stiffeners. Note that the cross-sectional areas for the stiffeners are not all the same, as noted in the box beside the figure. The thickness, t, of each web is the same. The location of the centroid has been computed for you and is included in the figure. a) (5 pts) Determine the area moments of inertia ly, Iz and Iyz. Express them in terms of L, A, and/or t. b) (10 pts) The location of the horizontal position of the shear center is defined by the parameter 'd' as shown in the sketch below. Set up a system of equations that will permit solution of d, in terms of the given geometry L, A, and/ort. These equations may involve only the geometric constants L, A, and/or t as well as the vertical shear resultant V and the shear flows 91, 92, 93, and q4 (use nomenclature and sign conventions for the shear flows given in the sketch). Simplify the equations appropriately. [Hint: you will need a system of five equations.] Note: you are not asked to solve the system of equation above. GEOMETRY + 3. t t t A N COORDINATE AXES L/2 L/3 2L/3 82 SHEAR FLOW NOMENCLATURE, SIGNS 8 3 V d: describes position of shear center "X" A = A | |A = A || A || A 1. (15 pts) An idealized box beam structure has a single-cell, closed cross-section, square shape. There are four stiffeners. Note that the cross-sectional areas for the stiffeners are not all the same, as noted in the box beside the figure. The thickness, t, of each web is the same. The location of the centroid has been computed for you and is included in the figure. a) (5 pts) Determine the area moments of inertia ly, Iz and Iyz. Express them in terms of L, A, and/or t. b) (10 pts) The location of the horizontal position of the shear center is defined by the parameter 'd' as shown in the sketch below. Set up a system of equations that will permit solution of d, in terms of the given geometry L, A, and/ort. These equations may involve only the geometric constants L, A, and/or t as well as the vertical shear resultant V and the shear flows 91, 92, 93, and q4 (use nomenclature and sign conventions for the shear flows given in the sketch). Simplify the equations appropriately. [Hint: you will need a system of five equations.] Note: you are not asked to solve the system of equation above. GEOMETRY + 3. t t t A N COORDINATE AXES L/2 L/3 2L/3 82 SHEAR FLOW NOMENCLATURE, SIGNS 8 3 V d: describes position of shear center "X" A = A | |A = A || A || A