Simply supported in both ends - Point load in any position

Table 7 Simply supported in both ends Point load in any position
$M (x)$	$= \frac{P \cdot b \cdot x}{L}$	for: $x \leq a$	Click to make a calculation...
	$= \frac{P \cdot a \cdot (L - x)}{L}$	for: $x \geq a$
$u (x)$	$= \frac{P \cdot b \cdot L \cdot x}{6 \cdot E \cdot I} \cdot [1 - {(\frac{b}{L})}^{2} - {(\frac{x}{L})}^{2}]$	for: $x \leq a$
	$= \frac{P \cdot b}{6 \cdot E \cdot I \cdot L} \cdot [\frac{L}{b} {(x - a)}^{3} + (L^{2} - b^{2}) \cdot x + x^{3}]$	for: $x \geq a$
$M_{MAX}$	$= \frac{P \cdot a \cdot b}{L}$	for: $x = a$
$u (a)$	$= \frac{P \cdot a^{2} \cdot b^{2}}{3 \cdot E \cdot I \cdot L}$
$u (\frac{L}{2})$	$= \frac{P \cdot a \cdot (3 \cdot L^{2} - 4 \cdot a^{2})}{48 \cdot E \cdot I}$
$u_{MAX}$	at: $x = a \sqrt{\frac{1}{3} + \frac{2 b}{3 a}}$	for: $a > b$
	at: $x = L - b \sqrt{\frac{1}{3} + \frac{2 a}{3 b}}$	for: $x \geq a$
$γ_{A}$	$= \frac{P \cdot L \cdot b}{6 \cdot E \cdot I} \cdot (1 - \frac{b^{2}}{L^{2}})$
$γ_{B}$	$= - \frac{P \cdot L \cdot a}{6 \cdot E \cdot I} \cdot (1 - \frac{a^{2}}{L^{2}})$

Table 7 Simply supported in both endsPoint load in any position