Isosceles right triangle cross section4/10/2024 The base of S is the region enclosed by the parabola y 2 - 3 x2 and the. Find the volume V of the described solid S. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. The base of S is an elliptical region with boundary curve 16 x 2 + 25 y 2 400. Integrating curvatures over beam length, the deflection, at some point along x-axis, should also be reversely proportional to I. Find the volume V of the described solid S. Therefore, it can be seen from the former equation, that when a certain bending moment M is applied to a beam cross-section, the developed curvature is reversely proportional to the moment of inertia I. Thus their combined moment of inertia is: These triangles, have common base equal to h, and heights b1 and b2 respectively. The moment of inertia of a triangle with respect to an axis perpendicular to its base, can be found, considering that axis y'-y' in the figure below, divides the original triangle into two right ones, A and B. This can be proved by application of the Parallel Axes Theorem (see below) considering that triangle centroid is located at a distance equal to h/3 from base. The moment of inertia of a triangle with respect to an axis passing through its base, is given by the following expression: Where b is the base width, and specifically the triangle side parallel to the axis, and h is the triangle height (perpendicular to the axis and the base).
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