Problem. A beam is under dead and live loads as shown in the figure below. The load values of each student are provided in the table. Select the lightest W section of Grade $50$ steel under the following conditions:

Continuous lateral support

Lateral supports at the ends

Lateral supports from the concentrated load points and the ends

For three conditions, identify the followings:

a$.$ Design the section using SAP$2000$;

b$.$ Design the section using hand calculation. Use $M_u,$ and $C_b$ from SAP$2000.$

c$.$ Compare the values between SAP$2000$ and hand calculations in a table.

d$.$ Discuss the influence of lateral support on the design.

Content of the homework submission:

$(1)$ SAP$2000$ views showing your loads of dead and live

$(2)$ Moment diagram using the factored load combination. Indicate the load combination used.

$(3)$ SAP$2000$ design for three cases.

$(4)$ Hand calculation result for three cases.

$(5)$ Comparison table for hand calculation and SAP$2000$ and discuss the results.

Wind load $=3$ kips$-$ft and Point load $=35$ kips