Stress
Stress is force applied on cross-sectional area.
Stress is the ratio between applied force and cross-sectional area where the applied force is acting.
Normal Stress
Normal stress can be expressed as
σ = FN / A (1)
where
σ = normal stress (N/m2, Pa, psi)
FN = applied force perpendicular to the area - Normal force (N, lb)
A = cross-sectional area (m2, in2)
Shear Stress
Shear stress can be expressed as
τ = FV / A (2)
where
τ = shear stress (N/m2, Pa, psi)
FV = applied force in plane of the area - Shear force (N, lb)
Example - Normal Stress in a Column
A 10000 N force is acting in the direction of a British Universal Column UB 152 x 89 x 16 with cross sectional area 20.3 cm2. The normal stress in the column can be calculated as
σ = (10000 N) / ((20.3 cm2) (0.0001 m2/cm2)
= 4926108 Pa (N/m2)
= 4.9 MPa
The Yield strength - the amount of stress that a material can undergo before moving from elastic deformation into plastic deformation - is typical 250 MPa for steel.
Example - Shear Stress in a Beam with Point Load
For a beam with single point load supported on both ends - the shear force Fv (or V in the figure above) is equal in magnitude to support force R1 or R2.
Reaction forces can be calculated due to moment equilibrium around support 1
F L / 2 = R2 L (4)
R2 = F / 2 (5)
R1 = R2 = F / 2 (6)
For a 10000 N point load perpendicular on a beam similar to the example above - supported at both ends - the magnitude of the reaction and shear forces can be calculated as
R1 = R2
= V1
= V2
= (10000 N) / 2
= 5000 N
= 5 kN
The shear stress can be calculated as
τ = (5000 N) / ((20.3 cm2) (0.0001 m2/cm2)
= 2463054 Pa
= 2.5 MPa
Related Topics
-
Mechanics
The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more. -
Statics
Forces acting on bodies at rest under equilibrium conditions - loads, forces and torque, beams and columns.
Related Documents
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Beams - Fixed at Both Ends - Continuous and Point Loads
Stress, deflections and supporting loads. -
Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads
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Beams - Supported at Both Ends - Continuous and Point Loads
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Stress in Thick-Walled Cylinders or Tubes
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Stress in Thin-Walled Cylinders or Tubes
Hoop and longitudinal stress thin-walled tubes or cylinders. -
Stress, Strain and Young's Modulus
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Young's Modulus, Tensile Strength and Yield Strength Values for some Materials
Young's Modulus (or Tensile Modulus alt. Modulus of Elasticity) and Ultimate Tensile Strength and Yield Strength for materials like steel, glass, wood and many more.
