Development of Flexiblity Matrix Problem 3 - Flexibility Method in Matrix Form

TL;DR

This lesson focuses on solving a problem related to the development of the stiffness matrix, considering two coordinates and two hinges.

Transcript

hello students welcome to the lesson four of the chapter three on the subject advanced structural analysis so in this lesson let us solve the third problem of development of stiffness matrix so the problem given to us is like this so there are two coordinates and two hinges like this so i'll call this a hinge as a medium now we have to develop the ... Read More

Key Insights

• ❓ The stiffness matrix is developed for a structure with two coordinates and two hinges.
• 💁 Unit forces and displacements provide information about the stiffness and flexibility elements.
• ❓ The directions of displacements are considered when determining the stiffness and flexibility values.
• ❓ The standard formulas used in solving the problem involve coefficients such as l/6EI and l/3EI.
• #️⃣ The size of the stiffness and flexibility matrices is determined by the number of coordinates.
• 🇦🇪 The problem involves applying unit forces in different directions to determine the matrix elements.
• 💁 The flexibility matrix is complementary to the stiffness matrix, providing information about displacements given unit forces.

Questions & Answers

Q: What is the problem being solved in this lesson?

The problem involves developing the stiffness matrix for a structure with two coordinates and two hinges.

Q: How is the size of the stiffness and flexibility matrices determined?

The size of the matrices is determined by the number of coordinates, in this case, it is 2x2.

Q: What are the elements of the stiffness matrix based on unit forces?

The stiffness elements are determined by applying unit forces in the direction of each coordinate and noting the resulting displacements.

Q: How are the directions of displacements considered in the stiffness and flexibility elements?

The directions of displacements are considered by referencing them with respect to the deflected shape, from the horizontal to the deflected shape.

Summary & Key Takeaways

• The lesson discusses the problem of developing the stiffness matrix for a structure with two coordinates and two hinges.

• The size of the stiffness matrix and flexibility matrix is determined by the number of coordinates.

• Unit forces and displacements are applied to each coordinate to determine the stiffness and flexibility elements.