Practice Question: Find Maximum Compressive Stress at a Beam Section

---

---

Solution

Taking sum of the moments about B:

\[∑M_B  = 0\]

\[R_A (10) – 10(3) = 0\]

\[R_A  = 3\, kips = 3000\, lb\]

Calculating bending moment at section a-a:

\[M_a=  3000 (2.5)( 12)=90,000\, lb-in\]

Now, Moment of Inertia for given section by:

Width of beam at section a-a = \(b\) = 10 in
Depth of beam at section a-a = \(h\) = 10 in

Moment of Inertia for rectangular section:

\[I=  \frac{bh^3}{12}\]

\[I=  \frac{10(10)^3}{12}\]

\[I=833.3 \,in^4\]

\[σ=\frac{Mc}{I}\]

\[σ=\frac{90000(5)}{833.3}\]

\[σ=540\,psi\]
 

---