Force method for analysis of propped cantilever beams

In the video below, I explained the application of force method for analyzing indeterminate beams of type "Propped cantilever beams"

Let us see another example problem, which is slightly more difficult.

This is the example of a non-prismatic propped cantilever. Non-prismatic beam is a beam whose cross-section is not uniform throughout. In the above figure the cross-section has moment of inertia of '2I' in the first 3m and 'I' in the next 2m. Let us say the fixed end is A and the prop is provided at B.

The deflection diagram (or elastic curve) looks as shown below. Note that there is some slope at B, but deflection is zero at B. whereas at A, both deflection and slope are zero. We can conclude that the vertical distance of B (after deformation) will be zero from the tangent at A (tangent at A is horizontal line AB). This is the compatibility condition for this problem.

From Moment area theorem-II we can conclude that the moment of M/EI diagram is zero about B.For drawing the M/EI diagram we have to draw 1) M-diagram or BMD for R_B and 2) M-diagram or BMD for given loading, and then add them up. The figure below shows the M-diagram and M/EI diagram due to R_B. At the section where cross-section changes suddenly, there will be two values of M/EI diagram, one using 2I in place of I, and another using I in place of I. Note the change in shape of M/EI diagram due to non-prismatic nature of beam

Similarly, the M-diagram (BMD) due to UDL is drawn and when divided with EI it give M/EI diagram. Again, due to the non-prismatic nature, the M/EI diagram has a sharp jump at the place where I is changing.

For determining the moment of the M/EI diagrams due to R_B and UDL, we need the knowledge of areas and centroids of the figures as shown below.

Using the above areas and centroids the moment about B of the M/EI areas between A and B can be calculated as shown below

After determining R_B, other support reactions V_A and M_A can be obtained based on vertical equilibrium equation and moment equilibrium equation. By this we should get, V_A= 47.89 kN and M_A=51.75 kN-m

INtroduction to arches and their analysis

The following video lecture introduces undergraduate civil engineering student to the world of arch structures and their analysis

Procedure for Creating an MCQ type online Examination in Moodle based LMS

 THe following series of videos guide you through the step by step procedure for creating an online examination through Moodle based LMS

Overview:

Step1: 

 

Step 2: 

Step 3: 

Step 4: 

 While importing the questions, ensure that under Import>General> the appropriate category is selected. To avoid database errors during parsing, it is recommended to use Notepad++ as the text editor for importing

Step 5: 

     

  **Note: Under the quiz settings< Grade settings<Attempts: Restrict the number of attempts to 1 

Finally you can preview your quiz to ensure compliance

Procedure to Import questions from word document to moodle

The video below shows the procedure for importing questions from word by converting the format to GIFT format of Moodle

       https://drive.google.com/open?id=15LZ3DYrYb7L4JBp-b0-9VtPv_mKiDvjR

Limit State Design of Industrial Gantry Girder

The following videos show the explanations for the design steps of an Industrial Gantry Girder, as per IS 800: 2007

1. Part I: Theory of design principles

       2. Part II: Illustrative example of Design of Gantry Girder

     3. Part III: Illustrative example of design checks on a Gantry Girder section

Application of ILDs for critical load analysis

Application of ILDs for static/ moving loads beyond single unit concentrated load

         ILD are drawn for a single unit concentrated load travelling on the span/ structure. In the following video, I tried to explain the application of concept of ILD to the analysis of static/moving loads other than unit load, other than concentrated loads, and for multiple loads.