**Problem F6–20: Determine the Reactions at Point D**In this problem, a structural frame is depicted consisting of a beam ABCD. The beam is supported with a hinge at point A and a roller at point D. - **Points and Dimensions:** - Point A is positioned at the base left of the structure with a height of 4 meters leading to point B. - The horizontal section BC is 12 meters long, divided into four equal segments of 3 meters each with supports or points at B and D. - Point D is at the same horizontal level as point C, at the far right end of the beam.- **Forces Acting on the Beam:** - A downward force of 10 kN is applied directly downward at point B. - Another downward force of 15 kN is applied directly at point C.The problem requires determining the reactions at point D due to these applied forces. The diagram suggests static equilibrium analysis where the sum of moments and forces needs to be balanced around the supports.

Draw the free-body diagrams of all members AB, BC and CD.Consider the diagram BC, apply moment equilibrium about C. By9-106-153=0By=11.67 kN Consider the diagram AB, apply moment equilibrium about A. -Bx4+By3=0Bx=34By=3411.67Bx=8.75 kN Apply force equilibrium in vertical direction. By-10-15-Cy=011.67-10-15-Cy=0Cy=-13.33 kN Apply force equilibrium in horizontal direction. Cx=BxCx=8.75 kN Consider the diagram CD, apply force equilibrium in horizontal and vertical directions. Dx=CxDx=8.75 kNAnd,Dy=CyDy=-13.33 kN Apply moment equilibrium about D. -MD+Cx4=0MD=8.75×4MD=35 kNm Therefore, the horizontal reaction is 8.75 kN backward, vertical reaction is 13.33 kN upward and moment is 35 kNm CCW.