A heavy air-conditioning system is to be mounted on the center of the roof of a building. Model the roof H a as a square

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A Heavy Air Conditioning System Is To Be Mounted On The Center Of The Roof Of A Building Model The Roof H A As A Square 1 (240.8 KiB) Viewed 33 times

A heavy air-conditioning system is to be mounted on the center of the roof of a building. Model the roof H a as a square plate of sides a=100m, and uniform thickness h=0.05m that is simply-supported on all four sides. The roof is made of an isotropic, linear elastic material with Young's modulus E = 2.1x10¹¹ N/m² and Poisson's ratio v = 0.3. The weight of the air-conditioner can be taken as a uniform distributed area load of o, = 500,000 N/m² acting over a centrally located square region of sides b = 10m (the shaded region in the figure). Due to concerns about the structural integrity of the floor, it is decided that a line elastic foundation (of modulus k (N/m²)) will be placed along the midline along the z-direction under the floor as shown. What should the elastic foundation modulus be so that the maximum roof deflection is reduced to one-half that of the case without the line foundation? a y Use the Rayleigh-Ritz method with the following bag of one-parameter candidate displacements: Uy(X,Z) = A₁ sin[¹X] sin[¹Z] a [Hint: See if you can apply any simplifying approximations that are reasonable and which will make your algebraic problem a lot easier to handle.] N b