A Steel Beam with a Rectangular cross section is to support a lateral load of $1200l{b}_{?}$ at its free end as shown in the figure.

a$)$ Calculate the Maximum Bending Stress, b$)$ Maximum Shear Stress and c$)$ Maximum Deflection

Given:

Material: Steel with:

$S_Y=36,000$

Modulus of Elasticity, $E=29{10}^6$

$L=$ Length, $L=6\mathrm{.}5ft.$

Section Geometry: Prismatic Rectangular Bar with $B={1\mathrm{.}75}^{\text{'}\text{'}},H={3\mathrm{.}5}^{\text{'}\text{'}}$

$I=(\frac{1}{12})B{H}^3$

Solution:

Bending Stress: $=+-\frac{Mc}{\text{I}}$

Where:

$=$ Bending Stress

$M=$ Bending Moment

$I=$ Area Moment of Inertia

$C=$ Distance from the Neutral Axis

$I=(\frac{1}{12})B{H}^{}$

Maximum Shear Stress $=$

Maximum Deflection $($for this Type of Beam and this Type of Loading ONLY$)=$

${}_{\text{M}\text{a}\text{x}\text{.}}=F\frac{L^3}{3}EI$