Problem 541
The 18-ft long floor beams in a building are simply supported at their ends and carry a floor load of 0.6 lb/in². If the beams have W10 × 30 sections, determine the center-line spacing using an allowable flexural stress of 18 ksi.
 

Problem 540
Timbers 8 inches wide by 12 inches deep and 15 feet long, supported at top and bottom, back up a dam restraining water 9 feet deep. Water weighs 62.5 lb/ft³. (a) Compute the center-line spacing of the timbers to cause f_b = 1000 psi. (b) Will this spacing be safe if the maximum f_b, (f_b)_max = 1600 psi, and the water reaches its maximum depth of 15 ft?
 

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