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Text-book Solutions

SOM, Solid Mechanics, Fracture Mechanics, Statics and Dynamics

This page addressess the analytical solution of text-books in the field of Strength of Materials, Solid Mechanics, Engineering Mechanics, Mechanical Vibrations, Kinematics & Dynamics of Mechanisms and Machinery...

Buckling Calulation - Fixed Beam with Lateral Loads

Buckling Fixed Beam

Buckling Fixed Beam

Buckling Fixed Beam

Rod sliding against fricctionless wall and ground

While this problem may look trivial, the solution requires good experience in solving dynamics problem. The application of moment balance about sliding contact point will not yield desired result. Frictionless Sliding Rod

Direction of Reaction Force on Inclined Plane

This type of situation is very frequently encountered while solving statics and dynamics problems. What is the angle made by normal reaction with inclined plane or what is the component of gravity force perpendicular to the inclined plane? Just remember the theorem: "The angle between two lines is equal to angle between perpendicular to those lines".

Inclined Plane

Mechanical Vibrations: Lagrangian Approach

Lagrangian approach is a powerful and straightforward method to derive equation of motion (EOM) for complex systems. The EOM for pring-mass-damper pendulum (also known as "sprung pendulum") is described below.

Inclined Plane

Inelastic Collision and Spring Compression

Collision is based on conservation of momentum and loss of energy defined by coefficient of restitution. This solution describes a case where one of the colliding objects is attached to a spring.

Inelastic Collision

Inelastic Collision

Crack Growth Calculations - Fracture Mechanics

Paris law is widely used in fracture mechanics calculations for number of cycles of variable loading required for crack to grow to critical size. Note that the rate of growth of crack per cycle, da/dN = A * δKm. Very often m is not an integer. The unit of δK is [MPa.m0.5]. Hence, special precautions should be taken to use consistent units for A, m and δK.

Fracture Mechanics

4-Bar Mechanism with Slider

Four bar slider

4-Bar Mechanism with Coupler Point

Four bar coupler point
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