GENERAL INSTRUCTIONS FOR THE FOLLOWING PROBLEM$($S$)$: USE THE LAST $2$ DIGITS OF YOUR STUDENT ID TO ESTABLISH

YOUR GENERIC DIMENSIONLESS DESIGN PARAMETERS TO BE USED FOR EACH PROBLEM. FILL THE TABLE SHOWN BELOW

AS PER THE EXAMPLE PROVIDED. WRONGLY CALCULATING ANY PARAMETER WILL RESULT IN A $50\%$ DEDUCTION OF THE

PROBLEM TOTAL SCORE FOR NOT FOLLOWING INSTRUCTIONS.

SOLVE THE FOLLOWING PROBLEMS. REMEMBER TO SHOW ALL YOUR WORK AND ASSUMPTIONS. $(65$ PTS$.)$

INSTRUCTIONS: Multiply ALL dead loads by B and ALL live loads by C$,$ where B and C your previously calculated

GDVs$.$ Multiply ALL dimensions shown by the corresponding GDVs$,$ where applicable.

a$.$ Assuming the following loading values, draw the beam considering the ultimate load combination, $U=1\mathrm{.}2DL+1\mathrm{.}6LL.$

Remember to multiply the loads depicted by your corresponding GDVs$,$ as instructed above. $(10$ pts $.)$

$P_{DL1}=12kB,P_{L1}=3kC,P_{DL2}=2kB,P_{L2}=0k,w_{DL}=0\mathrm{.}5\frac{k}{f}tB,w_{LL1}=0\mathrm{.}75\frac{k}{f}tC,w_{LL2}=1\mathrm{.}0\frac{k}{f}tC$

b$.$ Draw the appropriate Free Body Diagram for the beam shown depicting the

ultimate loads. $(5$ pts$.)$

c$.$ Obtain the reactions for the beam. $(7$ pts$.)$

d$.$ Draw the moment diagram for the beam. Identify the maximum and

minimum values of the diagram. $(7$ pts$.)$

e$.$ In reference to the previous problem, assume the ultimate maximum

positive moment $($under the $P_{DL}$ load, $M_u{?}_u)$ is $280$ kft and the ultimate

maximum negative moment $($over the pin support $M_u)$ is $140$ kft $.$ Design the

non$-$rectangular $\frac{R}{C}$ beam, assuming the cross section shown $($use $f_c^{\text{'}}=5$ksi

and $f_y=60$ksi $).$ For both cases, draw a sketch of the previously designed

reinforced sections $($one for $M_u^{+}$ and another for $M_u^{-}$