For the left figure below replace the distributed loads by a

For the left figure below, replace the distributed loads by an equivalent resultant force and a couple moment acting at point A. (See the right figure below.) Let a -3.90 m, w -6.00 kN/m, and w 5.00 kN/m R.A Calculate the resultant force, FR, and the couple moment, MR,A. Don\'t forget to include the appropriate signs Express your answers numerically in kilonewtons and kilonewton-meters to three significant figures separated by a comma. View Available Hint(s) FR , MR,A= 7.8,-91.26 kN, kN-m SubmitP Previous Answers X Incorrect; Try Again; no points deducted Term 1: Check your signs. Part E This question will be shown after you complete previous question(s)

Solution

For the triangular UDL, total effective force (F₁) = 0.5 x w₁ x a = 0.5 x 6 x 3.9 = 11.7 kN

Location of total effective force of triangular UDL from end A (d₁) = a/3 = 3.9/3 = 1.3 m

For the rectangular UDL, total effective force (F₂) = w₂ x a = 5 x 3.9 = 19.5 kN

Location of total effective force of rectangular UDL from end A (d₂) = a + a/2 = 3a/2 = 3 x 3.9 / 2 = 5.85 m

Taking moments about A,

F₂ x d₂- F₁x d₁ = M_RA

=> 19.5 x 5.85 - 11.7 x 1.3 = M_RA

=> M_RA = 98.865 kNm

Equating the total vertical forces,

F₁ - F₂ = F_R

=> F_R = 11.7 - 19.5

=> F_R = -7.8 kN