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A fixed-end beam is subjected to a concentrated load ($P$) as shown in the figure. The beam has two different segments having different plastic moment capacities ($M_P, 2M_P$) as shown.

The minimum value of load ($P$) at which the beam would collapse (ultimate load) is

  1. $7.5 \: M_P/L$
  2. $5.0 \: M_P/L$
  3. $4.5 \: M_P/L$
  4. $2.5 \: M_P/L$
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