Problem 536
A simply supported beam 10 m long carries a uniformly distributed load of 20 kN/m over its entire length and a concentrated load of 40 kN at midspan. If the allowable stress is 120 MPa, determine the lightest W shape beam that can be used.
 

Problem 535
A simply supported beam 24 ft long carries a uniformly distributed load of 2000 lb/ft over its entire length and a concentrated load of 12 kips at 8 ft from left end. If the allowable stress is 18 ksi, select the lightest suitable W shape. What is the actual maximum stress in the selected beam?
 

Problem 01
$\dfrac{dr}{dt} = -4rt$,   when   $t = 0$,   $r = r_o$
 

Solution 01
$\dfrac{dr}{dt} = -4rt$

$\dfrac{dr}{r} = -4t\,dt$
 

Linear Equations of Order One
Linear equation of order one is in the form
 

The general solution of equation in this form is
 

The differential equation
 

is an exact equation if
 

If the function f(x, y) remains unchanged after replacing x by kx and y by ky, where k is a constant term, then f(x, y) is called a homogeneous function. A differential equation
 

 
is homogeneous in x and y if M and N are homogeneous functions of the same degree in x and y.
 

The depreciation charge and the total depreciation at any time m using the sum-of-the-years-digit method is given by the following formulas:
 

Depreciation Charge:

Total depreciation at any time m

Where:
FC = first cost
SV = salvage value
n = economic life (in years)
m = any time before n (in years)
SYD = sum of years digit = 1 + 2 + ... + n = n(1 + n)/2