Evaluate the beam shown in Figure $3-1.$ Determine the capacity, check the live load deflection, and the total deflection. If the beam is not adequate, design a plate to reinforce the beam and recommend a construction procedure. The underside of the beam is approximately $10$ feet above the floor. Figure $3-1$: Simply supported beam with uniform load and concentrated load

Details of the structure:

Beam W $1214$

Steel grade: A$36$

Young's modulus: $29,000$ ksi

Dimensions

Length, $L,$ is $24$ feet

Location of the concentrated loads, a$,$ is $6$ feet

Loads

O Concentrated, $P,$ is $2000lb$

Distributed, w

Dead load is $120l\frac{b}{f}t$

Live load is $200l\frac{b}{f}t$

Deflection requirements

Live load is L$/360$

Total load is L$/240$