Stresses and Strains Beams and Loads Bending Stresses

1. *Load*: External forces applied 1. *Beams*: Structural 1. *Bending stresses*: Stresses

to a material. members that resist loads by caused by bending moments in
2. *Stresses*: Internal forces bending. beams.
resisting deformation. 2. *Types of beams*: 2. *Theory of simple bending*:
3. *Types of stresses*: Tensile, Cantilever, simply supported, Assumptions and derivation of the
compressive, shear, etc. overhanging, etc. bending equation.
4. *Strains*: Deformations 3. *Loads*: External forces 3. *Bending equation*: M/I = E/R =
resulting from stresses. applied to beams. f/y, where:
5. *Types of strains*: Linear, 4. *Types of loads*: Point - M = bending moment
volumetric, etc. loads, uniformly distributed - I = moment of inertia
loads (UDL), etc. - E = modulus of elasticity
- R = radius of curvature
Elasticity and Elastic Constants
Shear Force and Bending - f = bending stress
1. *Elasticity*: Ability of a
Moment - y = distance from neutral axis
material to return to its original
shape after deformation. 1. *Shear force*: Force that
causes shear deformation. Bending Stress Diagram
2. *Elastic limit*: Maximum
2. *Bending moment*: Moment 1. *Bending stress distribution*:
stress a material can withstand
that causes bending Variation of bending stress across
without permanent deformation.
deformation. a beam's cross-section.
3. *Hooke's Law*: Stress is
proportional to strain within the 3. *Shear force diagram*:
Graphical representation of Calculation of Maximum Bending
elastic limit.
shear force along a beam. Stress
4. *Elastic constants*:
4. *Bending moment diagram*: 1. *Rectangular sections*:
- *Young's modulus*:
Graphical representation of Calculation of maximum bending
Measures stiffness.
bending moment along a beam. stress.
- *Modulus of rigidity*:
2. *Circular sections*: Calculation
Measures shear stiffness.
Bending Moment and Shear of maximum bending stress.
- *Bulk modulus*: Measures
Force Diagrams 3. *T-sections*: Calculation of
resistance to volume change.
1. *Cantilever beams*: Beams maximum bending stress.
- *Poisson's ratio*: Measures
lateral strain. fixed at one end and free at
the other. Section Modulus
2. *Simply supported beams*: 1. *Definition*: Ratio of moment of
Stress-Strain Diagram Beams supported at both ends inertia to distance from neutral
1. *Nominal stress*: Average . axis.
stress calculated using original 3. *Beams with overhanging 2. *Section modulus for*:
cross-sectional area. portions*: Beams with portions - Rectangular sections
2. *Yield point*: Stress at which extending beyond supports. - Circular sections
plastic deformation begins. 4. *Point loads and UDL*: - I-sections
3. *Plastic stage*: Region of Different types of loads
permanent deformation. applied to beams. Slope and Deflection
4. *Ultimate strength*: Maximum 1. *Slope*: Angle of rotation of a
stress a material can withstand. beam's cross-section.
5. *Working stress*: Allowable 2. *Deflection*: Vertical
Columns and Struts
stress in a material. displacement of a beam.
1. *Columns*: Vertical structural
6. *Breaking stress*: Stress at
members that resist compressive
failure.
loads. Factors Affecting Strength of a
7. *Factor of safety*: Ratio of
2. *Struts*: Structural members Column
ultimate strength to working
that resist compressive loads, often 1. *Material properties*: Strength,
stress.
used in trusses. stiffness, and stability.
2. *End conditions*: Fixed, pinned,
Additional Topics Types of Columns or free ends.
1. *Stress on an oblique plane*: 1. *Short columns*: Columns that 3. *Effective length*: Length of
Stresses on inclined planes. fail by crushing. column between points of zero
2. *Principal stresses and 2. *Long columns*: Columns that moment.
principal strains*: Maximum and fail by buckling.
minimum stresses and strains. Euler's Formula
3. *Mohr's circle*: Graphical Slenderness Ratio 1. *Definition*: Formula to calculate
representation of stress states. 1. *Definition*: Ratio of effective buckling load of long columns.
length to radius of gyration. 2. *Limitations*: Only applicable to
2. *Importance*: Determines the long columns with certain end
column's susceptibility to buckling. conditions.

Buckling and Crushing Load Rankine-Gordon Formula

1. *Buckling load*: Load at which a 1. *Definition*: Formula to calculate
column buckles. buckling load of columns,
2. *Crushing load*: Load at which a considering both buckling and
column fails by crushing. crushing.
Torsion Springs
1. *Concept of torsion*: Twisting of a 1. *Concept of spring*: Elastic
shaft due to torque. member that stores energy.
2. *Difference between torque and 2. *Types of springs*: Helical, leaf,
torsion*: Torque is the external force, torsion, etc.
while torsion is the resulting
twisting effect. Spring Characteristics
1. *Stiffness*: Measure of spring's
Polar Moment of Inertia resistance to deformation.
1. *Definition*: Measure of a shaft's 2. *Deflection*: Displacement of
resistance to torsion. spring under load.
2. *Importance*: Used in torsion 3. *Strain energy*: Energy stored
calculations. in spring due to deformation.
Angle of Twist Proof Resilience
1. *Definition*: Angle of rotation of a 1. *Definition*: Maximum strain
shaft's cross-section. energy stored in a spring without
2. *Importance*: Used to calculate permanent deformation.
torsional deformation.
Close Coil Helical Springs
Torsional Rigidity 1. *Definition*: Springs with
1. *Definition*: Measure of a shaft's closely coiled helical shape.
resistance to twisting. 2. *Axial load*: Load applied along
2. *Importance*: Used to calculate the spring's axis.
torsional stiffness.
Laminated Springs (Semi-Elliptical
Torsion Equation Type)
1. *Derivation*: T/J = Gθ/L = τ/r, 1. *Definition*: Springs composed
where: of multiple layers of flat plates.
- T = torque 2. *Determination of number of
- J = polar moment of inertia plates*: Calculation based on load,
- G = shear modulus deflection, and material
- θ = angle of twist properties.
- L = length of shaft
- τ = shear stress
- r = radius of shaft
2. *Significance*: Used to calculate
torsional stresses and deformations.

Comparison between Solid and

Hollow Shafts
1. *Strength*: Hollow shafts can be
stronger than solid shafts for same
weight.
2. *Weight*: Hollow shafts can be
lighter than solid shafts for same
strength.

Power Transmitted by Shaft

1. *Calculation*: Power = torque x
angular velocity.
2. *Importance*: Used to design
shafts for power transmission.

Mean and Maximum Torque

1. *Mean torque*: Average torque
transmitted by a shaft.
2. *Maximum torque*: Maximum
torque transmitted by a shaft.