Mass: amount of Matter of which a body is composed.
Force: 1N is the force required to cause a mass of 1 Kg to accelerate at a rate of 1 per second squared in the abscence of other force-producing effects.
Examples:
a 4Kg mass, sitting on a table, is constly applying 49.8m/s/s (Gravity). ie, 39.2Newtons of Force.
* On the moon, the same 4Kg is applying only 41.62m^2 = 6.48N
* Weight:
Definition: the Force of Gravity being exerted on a body by the Earth.
Pascal:
The coefficient (ratio) of Force over Area.
The unit of Stress or Tension
When in pressure, called “Load”
in SI: P = Newton/1m^2
In US: Psi
* Tension:
Force = Tension / Area
In US: = ibs/in^2
Bending Moment:
The product of a quantity and its perpendicular distance from a reference point.
M = dF
ie: Moment = momentArm * Force
The bending moment causes bending stresses in the form of compression at the top and tension at the bottom, below the neutral axis. The Tension will equal the Compression. One simply designs for the material's weakest E.
In an isotropic material (eg: steel) the material's compression E is the same as the material's tension E.
In an an-isotropic material (eg: concrete) the concrete in tension will immediately fail, causing the steel to pick up the tension. The cracks will never pass the netral axis as the concrete is in tension above it.
M@15 = wx/2.(l-x) = (5015)/2 x 30-15 = 375 x 15 = 5625#ft moment
* M@10 = w10/2.(l-10) = (5010)/2 x 30-20 = 250 * 10 = 2500#ft moment
Strain:
Simply a measure of how much member gets longer or shorter under tension/compression.
Stress:
Definition: “The ratio of applied load to the cross-sectional area of an element”.
About:
There are different forms of stress: Compressive, Tensile, Bearing, and Shear stress.
Equation:
General equation: F = F/A,
Compressive stress: fc = F/A
Tensile stress: ft = F/A
Bearing stress: fB = F/A
Shear stress: fv=F/A
Axial or Bending stress: M y / I
Unit:
SI: kg/mm^2
SI: N/m^2
US: K/in^2 (ksi)
Example:
Tensile Stress:
50,000# hung on a steel rod with area 0.75in^2
⇒ 50k# * 0.75 = 50ksi
Compressive Stress:
50,000# loaded on a footing of 3ft^2 ⇒ 50K#/(3636) = 38.58psi
* Bearing stress:
* 50#/ft on a 2“x12” beam, 20' long, sitting on a 3“ lintel.
* ⇒ F=(20'50#)/2, A = 1.5”x3“
fb = F/A = 500# / 4.5 = 111.12psi
Notes:
Shear forces act like scissors. Shear failure usually occur close to supports of beams of length <20ft.
The vertical and loaded Shear stresses which develop in a loaded beam depend on the values of the Bending Moemnt and Shear Force in the beam.