# Structural Engineering - Structural Mechanics, Analysis, Design

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## Tuesday, November 28, 2017

## Wednesday, November 22, 2017

## Tuesday, November 21, 2017

## Tuesday, November 7, 2017

## Sunday, May 14, 2017

### Redundant of curved(Circular) beam using Castigliano's theorem.

Hi,

Problem: The given beam consist of straight beam AC where A is fixed, and curved(circular) beam CE. Load P is horizontal. (a) Draw Free Body diagram (b) Write moment equations for AC and CE part. (c) Write the expression to find the redundant at E, using the Castigliano's theorem for deflection.

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Problem: The given beam consist of straight beam AC where A is fixed, and curved(circular) beam CE. Load P is horizontal. (a) Draw Free Body diagram (b) Write moment equations for AC and CE part. (c) Write the expression to find the redundant at E, using the Castigliano's theorem for deflection.

curved/Circular beam redundant using Castigliano's theorem |

Check the relevant books to buy.

## Saturday, April 29, 2017

### Characteristic Equation for a 4*4 Matrix (Eigenvalues)

Whenever a 4*4 matrix is given, and it is to find the characteristic equation. Always expand along the column or row, which has the maximum number of zeroes. Look for the solved example given below.

Given Matrix A is a 4*4 matrix, with 9, 7, 5 and 9 as the diagonal elements. First column contains the maximum zeroes, so expand along it. The final equation is the characteristic equation. Soling it gives 9, 5 and 7 as the eigenvalues.

Thanks for the visit!

Given Matrix A is a 4*4 matrix, with 9, 7, 5 and 9 as the diagonal elements. First column contains the maximum zeroes, so expand along it. The final equation is the characteristic equation. Soling it gives 9, 5 and 7 as the eigenvalues.

Thanks for the visit!

## Saturday, April 15, 2017

### Solved - Virtual Work Method - Deflection of Beam - Propped Cantilever with Internal hinge

Hi

Consider the compound beam shown in fig. EI is constant. Use the principle of Virtual Work. Determine the displacement at point D.

Please refer the image below for the solution.

Consider the compound beam shown in fig. EI is constant. Use the principle of Virtual Work. Determine the displacement at point D.

Please refer the image below for the solution.

Virtual Work Method - Deflection of beam - Propped cantilever with internal hinge |

Virtual Work Method - Deflection of Beam - Propped Cantilever with Internal Hinge |

## Tuesday, April 4, 2017

## Friday, March 24, 2017

### Solved -Shear Flow equation- Wooden Beam and Nail Spacing using

Hi,

Here is an example of solved problem, when you are asked to find the shear capacity of nailed wooden beams, or asked about the spacing of nails. Leave your suggestions or doubts in the comment box below.

a= 250 mm, b= 35 mm, c= 265 mm, d = 180 mm, and e= 300mm. Assume the sections are uniform along the length of the beam. Find:

Solution:

Thanks!

Here is an example of solved problem, when you are asked to find the shear capacity of nailed wooden beams, or asked about the spacing of nails. Leave your suggestions or doubts in the comment box below.

**Problem:**The two cross sections (a) and (b) of a wooden beam are shown below. Both are subjected to a vertical shear force of V. Each nail can support a shear force of 20 kN, and are spaced at 125 mm along the length of the beam. Section details:a= 250 mm, b= 35 mm, c= 265 mm, d = 180 mm, and e= 300mm. Assume the sections are uniform along the length of the beam. Find:

**(A)**Maximum applicable shear force on member (a)**(B)**Maximum applicable shear force on member (b)**(C)**Adjust the spacing of the weaker member for the maximum of the forces found in part (A) and part (B).Solution:

Thanks!

## Friday, March 17, 2017

## Thursday, December 22, 2016

### Force method for Indeterminate continuous Beam - Matrix Approach

Hi,

In force method of structural analysis,

Thanks You!

In force method of structural analysis,

- the first step is to find the Redundancy/indeterminacy of the structure. For example for the given beam in the following example there are total five number of support reactions, therefore the redundancy is 2.
- Second step is to convert the indeterminate structure into a basic determinate by replacing the the two of the unknown support reactions with redundants.
- Third step is to find out the displacements of the basic determinate structure along the redundants due to the given loading conditions.
- fourth step is to find out the flexibility matrix by applying the unit loads along the redundants and finding out the corresponding displacements at these two places.
- Next, form the equations as per the compatibility conditions and form the matrices.
- Solve the matrix problem to find out the unknown reaction forces.

**Example:**Let us consider a continuous beam with a total span of 10m, EI constant, udl acting on the first half and a couple acting at 7.5m from the left. There are hinge and roller support at B and C, while beam is fixed at the left end A. Find out the support reactions at B and C using the force method (matrix approach.)

Thanks You!

## Tuesday, November 29, 2016

### Tension member connected to Gusset plate(fail in Rupture/Fracture or yield?)

Hi,

A tension member - a rectangular plate of dimension 1/2"*8" connected with two rows of bolts, determine the bolt size so that the tension member fails in rupture but not yield. Steel of grade A36 grade is used.

It must be kept in mind that the capacity factors are different for the rupture and yield, its lower for finding the rupture capacity, the section where bolts are inserted into the member are considered critical. Solution is written in the image shown below.

A tension member - a rectangular plate of dimension 1/2"*8" connected with two rows of bolts, determine the bolt size so that the tension member fails in rupture but not yield. Steel of grade A36 grade is used.

It must be kept in mind that the capacity factors are different for the rupture and yield, its lower for finding the rupture capacity, the section where bolts are inserted into the member are considered critical. Solution is written in the image shown below.

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