Question

A simply supported beam of span \(6\,\mathrm{m}\) carries a central point load. If the plastic moment capacity is \(90\,\mathrm{kN\!-\!m}\), the collapse load is

• A. \(45\,\mathrm{kN}\)
• B. \(60\,\mathrm{kN}\)
• C. \(75\,\mathrm{kN}\)
• D. \(90\,\mathrm{kN}\)

Hint:

For a simply supported beam with a central point load, \[ \boxed{ W=\frac{4M_p}{L}. } \]

Answer 1

The Correct Option is B

Step 1: Recall the collapse condition. For a simply supported beam carrying a central point load, \[ M_p=\frac{WL}{4}, \] where \[ M_p=90\,\mathrm{kN\!-\!m}, \qquad L=6\,\mathrm{m}. \]

Step 2: Calculate the collapse load. \[ W = \frac{4M_p}{L} = \frac{4\times90}{6} = 60\,\mathrm{kN}. \] Hence, \[ \boxed{60\,\mathrm{kN}} \] is the correct answer. Therefore, \[ \boxed{(B)} \] is the correct answer.