Learning Goal To Use The Method Of Superposition To Calculate A Beam Deflection And Slope For Beams With Small Deflect 1 (57.31 KiB) Viewed 32 times
Learning Goal: To use the method of superposition to calculate a beam deflection and slope. For beams with small deflections, the assumptions for using the method of superposition apply: the deflections and slopes are linearly related to the load, and the deflections do not significantly change the original geometry of the beam. The deflections and slopes for beams subjected to multiple loads can then be found using linear combinations of known results for individual loads. Use the two loadings below and the principle of superposition to answer the following questions. V V W W₂ Load B -5w L4 V 384EI -w₁ L³ 0₁ 24EI w₁ L³ OB 24EI -5w₂ L4 768EI -3w₂ L³ 128EI 7w2 L³ 384EI
▼ Part A - Determine the load combination A beam is subjected to the loading shown (Figure 1) where wa = 1.8 kN/m and w = 2.8 kN/m. Describe the loading as a linear combination of the loads in the above table. Express your answers in kN/m. ▸ View Available Hint(s) IVE ΑΣΦ | | vec SAN ? W1, W2 = Submit kN/m
▸ Part A-Determine the load combination Part B - Deflection at the midpoint What is the deflection at the midpoint of the beam from Part A if E= 200 GPa and I = 4x10 cm* ? Let a positive deflection be upward. Express your answer with appropriate units to three significant figures. ▸ View Available Hint(s) HÅ ? v(2=4 m) = Value Units Submit Part C - Slope at A What is the slope at the left end of the beam from Part A if E = 200 GPa and I = 4x10¹ cm² ? Express your answer in radians to three significant figures. ▸ View Available Hint(s) 15.ΑΣΦ. Η vec ? 0A = radians
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