Part A Replace the distributed loading by an equivalent resultant force Suppose

Question

Part A Replace the distributed loading by an equivalent resultant force Suppose that w 3 kN/m and w2 5 kN/m Eigure 1) Determine the equivalent resultant force Express your answer to three significant figures and include the appropriate units. Enter positive value if the force is upward and negative value if the force is downward. IA FRVUnits Submit My Answers Give Up Part B Specify the location of the force on the beam, measured from the pin at A Express your answer to three significant figures and include the appropriate units. Figure 1 of! d= Value Units Submit My Answers Give Up

Explanation / Answer

Given,

w1 = 3 kN/m, w2 = 5 kN/m

A) Dividing total load into a UDL and UVL

Calculate the total load acting on the beam due to UDL

F1 = w1 x L = 3 x 6 = 18 kN

Calculate the total load acting on the beam due to VDL

F2 = 0.5 x (w2 - w1) x (L/2) = 0.5 x (5 - 3) x 3 = 3 kN

Calculate the resultant load.

F = F1 + F2 = 18 + 3 = 21 kN

B) Centroid of the UDL from point A

x1 = L/2 = 6/2 = 3 m

Locate the centroid of the VDL from point A

x2 = (L/2) + (2L/6) = 3 + 2 = 5 m

centroid of the resultant load measured from point A

x = (F1x1 + F2x2) / (F1 + F2) = [(18 x 3) + (3 x 5)]/ (21) = 3.286 m

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