## Cantilevered Beam

Calculate the deflection at the cantilevered beam's tip if a 7,000 N/m distributed load is applied. Assume E*I = 6.4x10^6 N*m^2.

##
__
__**Hint**

**Hint**

$$$\upsilon_{max}=\frac{-wL^{4}}{8EI}$$$

where
$$w$$
is the distributed load,
$$L$$
is the beam’s length,
$$E$$
is the modulus of elasticity, and
$$I$$
is the moment of inertia.

##
__
__**Hint 2**

**Hint 2**

The final answer should be negative to indicate a downward deflection.

Referencing the cantilevered beam slopes and deflections section in the FE handbook (or any other ref table), the deflection formula is:

$$$\upsilon_{max}=\frac{-wL^{4}}{8EI}$$$

where
$$w$$
is the distributed load,
$$L$$
is the beam’s length,
$$E$$
is the modulus of elasticity, and
$$I$$
is the moment of inertia.

$$$\upsilon_{max}=\frac{-7,000N/m\cdot (5m)^{4}}{8\cdot 6.4\times 10^6N\cdot m^2}$$$

$$$\upsilon_{max}=-\frac{4,375,000}{51,200,000}\:m=-0.085\:m$$$

(Note: the negative sign (-) indicates the deflection is downwards.)

-0.085 m