The body shown is a square with sides of length 2 m. A point force of 10 kN acts

Question

The body shown is a square with sides of length 2 m. A point force of 10 kN acts at the quarter point of the top edge of the square as shown at an angle of 45 to the horizontal. The object is at rest.

a) Calculate the horizontal and vertical components of the reactions at the supports.

b) Calculate the magnitude of the total reaction at the left hand support.

The body shown is a square with sides of length 2 m. A point force of 10 kN acts at the quarter point of the top edge of the square as shown at an angle of 45 to the horizontal. The object is at rest. a) Calculate the horizontal and vertical components of the reactions at the supports. b) Calculate the magnitude of the total reaction at the left hand support. c) (Explanation question) If the sides of the square were changed to 4 m (but the force remain unchanged), how would the answer to (b) above change? Calculations are not required in answering this question, but use of diagrams and writing down appropriate equations (without solving them) may aid the response

Explanation / Answer

Y-direction force balance:-

Ray + Rby = 7.07________________(eq.1)

X-direction force balance:-

Rax = 7.07 _______________(eq.2)

Moment balance about A:-

7.07* L - Rby * L - 7.07 * L/4 = 0

So, 7.07 - Rby - 7.07 * 1/4 = 0 _______________ (eq.3)

Rby = 5.30 KN

Ray = 1.77 KN

B. Magnitude = 7.29 KN

C. Now sides are 4m:

No change in reactions at any point or in any direction will occur. This is because there is no term of length in any of the 3 equations are present.

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