Answer the following in brief:
List out assumptions to derive of equation of simple bending.
- Beam is initially straight, and has a constant cross-section.
- Beam is made of homogeneous material and the beam has a longitudinal plane of symmetry.
- Resultant of the applied loads lies in the plane of symmetry.
- The geometry of the overall member is such that bending not buckling is the primary cause of failure.
- Elastic limit is nowhere exceeded and ‘E’ is same in tension and compression.
- Plane cross sections remains plane before and after bending
Define the following: Youngs modulus, shear modulus and bulk modulus.
- Young.s modulus: With in the elastic limit, the ratio of longitudinal stress to longitudinal strain is called young.s modulus.
- Bulk modulus: With in the elastic limit, it is defined as the ratio of Bulk stress to Bulk strain
- Rigidity modulus: With in the elastic limit, it is defined as the ratio of shearing stress to shearing strain.
Define factor of safety and what are factors to be considered to fix the value of it.
Factor of Safety (FoS) is a critical safety measure that determines how much additional load a structure, product, or system can handle beyond its normal operating conditions.
The higher the number of FoS, the safer the product or structure is. An FoS of 1 indicates that a structure or component will fail immediately when the design load is reached and cannot support any extra load.
Write down the mathematical expressions of equivalent bending moment and equivalent twisting moment.
\({M_e} = \frac{1}{2}\left( {M + \sqrt {{M^2} + {T^2}} } \right)\)
\({T_e} = \sqrt {{M^2} + {T^2}} \)
What is the difference between beam, columns and struts?
Define principal planes and principal stresses.
Principal Planes are defined as those mutually perpendicular planes within a stressed body where the shear stress is zero. On these planes, the stress is purely normal (i.e., perpendicular to the plane).
Principal Stresses are the normal stresses acting on these principal planes. They represent the maximum and minimum normal stresses possible at that point in the material.
Principal Stresses are the normal stresses acting on these principal planes. They represent the maximum and minimum normal stresses possible at that point in the material.
Define: Isotropic and anisotropic materials.
Isotropic materials have the same physical, chemical, thermal and electrical characteristics that are independent of orientation. This means that applying force or pressure anywhere will not result in the preferred direction of deformation. For example, if you apply stress to an isotropic material in any of the three spatial directions, it will behave the same way. Examples of isotropic materials include metals, plastics, and glass.
Anisotropic materials are characterized by the fact that their properties change in different directions. An example of an anisotropic material is wood. When mechanical force is applied to it, its behavior will differ depending on the direction in which the force is applied.
Define: Creep, fatigue and endurance limit.
Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating stresses (e.g., bridges, aircraft, and machine components). The term “fatigue” is used because this type of failure normally occurs after a lengthy period cf repeated stress or strain cycling.
Creep is the slow, permanent deformation of a solid material under constant stress over time, often at high temperatures, even below its yield strength, while the Endurance Limit (or Fatigue Limit) is the maximum stress a material can withstand for an infinite number of loading cycles without fracturing from fatigue. Creep involves gradual, time-dependent stretching (like in turbine blades), whereas endurance limit defines the threshold for resisting repeated, fluctuating loads (like in car axles) before fatigue failure occurs.
What is the difference between resilience and toughness?
Resilience is the ability of a material to absorb elastic (non-permanent) deformation energy and release it upon unloading. It's about returning to the original shape.
Toughness is the ability of a material to absorb energy (both elastic and plastic deformation) up to the point of fracture. It involves permanent deformation and damage absorption without breaking.
What is the difference between fracture and failure?
Fracture is the separation of a material or component into two or more pieces. It is the mechanism of breaking.
Failure is when a component or structure can no longer perform its intended function. Fracture is one way failure can happen, but not the only way.
Examples
- A steel beam yields a lot and bends permanently → failure (by excessive plastic deformation), no fracture
- A glass cup shatters when dropped → failure by brittle fracture
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