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 wn -3 kN/m and wp 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. FR Value Units Submit My Answers Give Up Part B Specify the location of the force on the beam, measured frormn the pin at A Express your answer to three significant figures and include the appropriate units. gure of 1 Submit My Answers Group 4' Continue 3 m

Explanation / Answer

Consider O as the midpoint of AB.
The net force due to the left rectangular section, F1 = W1 x AO
= 3 kN/m x 3 = - 9 N, which is acting at a distance 1.5 m from A.

The net force due to the right rectangular section, F2 = W1 x OB
= 3 kN/m x 3 = - 9 kN, which is acting at a distance of 4.5 m from A

The net force due to the upper right triangular section, F3 = 1/2 x OB x (W2 - W1)
= 0.5 x 3 x (5 - 3) = - 3 kN, which is acting at a distance of 5 m from A.

Resultant force, Fr = F1 + F2 + F3
= - 9 - 9 - 3
= - 21 kN

Consider the net torque about A
F1 x 1.5 + F2 x 4.5 + F3 x 5 + Fb x 6 = 0
Where Fb is the reaction force at B.
Substituting the values,
- 9 x 1.5 - 9 x 4.5 - 3 x 5 + Fb x 6 = 0
6 Fb = 69
Fb = 11.5 kN

Consider that the resultant force is acting at a position R from the point A.
Net torque about A is
Fr x R + Fb x AB = 0
- 21 x R + 11.5 x 6 = 0
R = 69/21
= 3.29 m

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