The frame shown below was analyzed in SAP $2000.$ The resulting moment envelope is shown. Determine the size and reinforcement necessary for beam $AB($marked in figure$)$ at the three points indicated in the figure $($two end points and midspan$).$ The size should remain constant and only the reinforcement varied in the three sections. Select reinforcing bars and draw the details carefully for each of the three sections. As a guide to size the beam you may use a reinforcement ration of approximately $70\%$ of the maximum allowed by the ACI $318$ code. Use $f_c^{\text{'}}=5,000$ psi and $f_y=60,000.$