Remember at D it's a roller which means the reaction of Dx is equal to zero

Chemistry

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Answer

You are correct to point out that if D is a roller support, then its horizontal reaction DxD_x is zero. Let's re-evaluate the support reactions with this corrected information.

Step-by-step solution

2 steps

Revised Given Information:

  • Uniformly distributed load (UDL) on beam CB: w=6 KN/mw = 6 \text{ KN/m}
  • Length of beam CB: LCB=10 mL_{CB} = 10 \text{ m}
  • Horizontal point load at B: Px=20 KNP_x = 20 \text{ KN} (acting to the right)
  • Height of columns CD and AB: H=10 mH = 10 \text{ m}
  • Support at D: Roller support (resists vertical force DyD_y, but Dx=0D_x = 0)
  • Support at A: Roller support (resists vertical force AyA_y, but Ax=0A_x = 0)
  1. Identify Reactions

    • At roller support D: Vertical reaction DyD_y. (Horizontal reaction Dx=0D_x = 0).
    • At roller support A: Vertical reaction AyA_y. (Horizontal reaction Ax=0A_x = 0).
  2. Apply Equilibrium Equations

    1. Sum of horizontal forces (∑Fx=0\sum F_x = 0): Assume forces to the right are positive. The only horizontal force applied to the frame is the 20 KN20 \text{ KN} load at B. Since both supports A and D are roller supports, they cannot provide any horizontal reaction. ∑Fx=20 KN=0\sum F_x = 20 \text{ KN} = 0 This equation is a contradiction (20 KN≠020 \text{ KN} \neq 0).

    Conclusion:
    If both supports A and D are roller supports, the structure cannot resist the 20 KN20 \text{ KN} horizontal load applied at B. This means the frame is unstable under this loading condition and cannot be in static equilibrium. Therefore, it is not possible to calculate the support reactions AyA_y and DyD_y under the assumption of static equilibrium with these support conditions and the given horizontal load.

    To proceed with a stable structure, one of the following would typically be required:

    • Support D is a pin support (as it appears in the original image), which can provide a horizontal reaction DxD_x.
    • The horizontal load of 20 KN20 \text{ KN} is not present or is resisted by another mechanism not shown.

    Please clarify the support conditions or if there's an alternative interpretation for the horizontal load.

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