In all programs, the basic units are Force (Lb, kip, N, kN, etc.), Length (ft, in, m, mm, etc.), Time (second), and Temperature (F, C). Mass is a derived unit. CSI programs do not use Lb or kip for mass units, they are only used for force units.
Weight has units of [F], where F is force. CONSISTENT mass units are given by [F/(L/T^2)], where L is length, T is time, and the mass units are simply force divided by UNIT acceleration.
When F = N, the consistent mass unit is N*s^2/m = kg.
When F = Lb(force), the consistent mass unit is Lb(force)*s^2/ft = slug.
This is the mass that gives a force of 1 Lb(force) under a unit acceleration.
This same mass, when accelerated by gravity g, gives a force (its weight) of 32.2 Lb(force).
The mass called Lb(mass) is not a consistent unit. 1 slug = 32.2 Lb(mass)
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\\ The basic units for all {new-tab-link:http://www.csiberkeley.com/}CSI{new-tab-link} Software include force (lbs, kip, N, kN, etc.), length (ft, in, m, mm, etc.), time (second), and temperature (F, C). [Mass|kb:Mass] is then derived from these values. Some notes which concern force and mass units are as follows: * lbs and kips are only used as force units, not mass units * Consistent mass units are force divided by unit acceleration, given as F/(L/T{^}2{^}), where L is length and T is time. Weight is a force. \\ \\ ** Given SI units, where force is in Newtons (N), the consistent mass unit is N*sec{^}2{^}/m = kg. \\ \\ ** Given US Customary, where force is in pounds (lbs), the consistent mass unit is lbs*sec{^}2{^}/ft = slug. Under a unit acceleration, a mass of one slug generates a one pound force. When accelerated by gravity (g), this same mass generates a force of 32.2 lbs. * The pound-mass unit is not a consistent unit, where 1 slug = 32.2 pound-mass. Additional information is available in the Wikipedia {new-tab-link:http://en.wikipedia.org/wiki/Pound |
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_(force)}Pound (force){new-tab-link} article. * Weight density has units of F/L{^}3{^} * Consistent mass density has units of (F/(L/ |
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T{^}2{^}))/ |
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The relationship between weight and mass is W = M * g, all in consistent units.
Likewise, the relationship between weight density and mass density is w = m * g.
Now, let's start with weight density w = 150 Lb/ft^3. Here "Lb" is a force, Lb(force), and convert it to mass density in kip-in units. Note that "kip" is also a force. Proceeding:
m = w / g = 150 Lb/ft^3 / (32.2 ft/s^2) = 4.658 Lb*s^2/ft^4 * (kip / 1000 Lb) * (ft / 12 in)^4 = 2.246E-7 kip*s^2/in^4
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L{^}3{^} = F*T{^}2{^}/L{^}4{^}
* The relationship between weight and mass, and weight density and mass density, is W = M * g, all in consistent units.
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** To convert weight density W = 150 lbs/ft{^}3{^} into mass density (kip-in), the calculation proceeds as follows:
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M = W / g = 150 lbs/ft{^}3{^} / (32.2 ft/sec{^}2{^}) = 4.658 lbs*sec{^}2{^}/ft{^}4{^} * (kip / 1000 lbs) * (ft / 12 in){^}4{^} = 2.246E-7 kip*sec{^}2{^}/in{^}4{^}
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