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42x

000653

2024-09-26

Second Element Using Bending Theory According to Mindlin

v_{x} (x) = 5 - 5 x

m_{x} (x) = \int v_{x} dx + m_{x, 0} = 5 x - \frac{5}{2} x^{2} + m_{x, 0}

m_{x, C} = m_{x} (1.5) = 9.167 = \int_{0}^{1} 5 x - \frac{5}{2} x^{2} + m_{x, 0} = {[\frac{5}{2} x^{2} - \frac{5}{6} x^{3} + m_{x, 0} x]}_{0}^{1} = 1.667 + m_{x, 0}

m_{x, 0} = m_{x} (1)^{+} = 9.167 - 1.667 = 7.5

m_{x} (1) = \frac{m_{x} (1)^{-} + m_{x} (1)^{+}}{2} = \frac{7.5 + 7.5}{2} = 7.5

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