Question

a) r1 = ? r2 = ? σmx = 0 σv = 0 σmr2 = 0 = 16r1 - (2500×12)-(5500×5) r1 = σv = 0=(r1 + r2)-(2500 + 5500) r2 =

Explanation:

Step1: Solve for \(R_1\) from moment - equilibrium equation

We have \(\sum M_{R_2}=0 = 16R_1-(2500\times12)-(5500\times5)\). First, calculate the right - hand side values: \(2500\times12 = 30000\) and \(5500\times5=27500\). Then the equation becomes \(16R_1-30000 - 27500=0\), or \(16R_1=30000 + 27500=57500\). So, \(R_1=\frac{57500}{16}=3593.75\).

Step2: Solve for \(R_2\) from vertical - force equilibrium equation

We know that \(\sum V = 0=(R_1 + R_2)-(2500 + 5500)\). Substitute \(R_1 = 3593.75\) into the equation: \(3593.75+R_2-(2500 + 5500)=0\). First, simplify the right - hand side: \(2500 + 5500 = 8000\). Then \(R_2=8000 - 3593.75 = 4406.25\).

Answer:

\(R_1 = 3593.75\), \(R_2 = 4406.25\)