Solution to Problem 534 | Economic Sections
Problem 534
Repeat Prob. 533 if the uniformly distributed load is changed to 5000 lb/ft.
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Problem 01 | Separation of Variables
Problem 01
$\dfrac{dr}{dt} = -4rt$, when $t = 0$, $r = r_o$
Solution 01
$\dfrac{dr}{dt} = -4rt$
$\dfrac{dr}{r} = -4t\,dt$
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Linear Equations | Equations of Order One
Linear Equations of Order One
Linear equation of order one is in the form
The general solution of equation in this form is
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Exact Equations | Equations of Order One
The differential equation
is an exact equation if
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Homogeneous Functions | Equations of Order One
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.
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Derivation of Formula for Sum of Years Digit Method (SYD)
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
Formulas in Engineering Economy
Formulas in Engineering Economy
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Separation of Variables | Equations of Order One
Given the differential equation
where $\,M\,$ and $\,N\,$ may be functions of both $\,x\,$ and $\,y\,$. If the above equation can be transformed into the form
where $\,f(x)\,$ is a function of $\,x\,$ alone and $\,f(y)\,$ is a function of $\,y\,$ alone, equation (1) is called variables separable.
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Elementary Differential Equations
Families of Curves
Equations of Order One
Elementary Applications
Additional Topics on Equations of Order One
Linear Differential Equations
Linear Equations with Constant Coefficients
Nonhomogeneous Equations: Undetermined Coefficients
Variation of Parameters
Inverse Differential Operators
Applications
Topics so far...
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Solution to Problem 533 | Economic Sections
Problem 533
A beam simply supported on a 36-ft span carries a uniformly distributed load of 2000 lb/ft over the middle 18 ft. Using an allowable stress of 20 ksi, determine the lightest suitable W shape beam. What is the actual maximum stress in the selected beam?
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