Design of small industrial building with gantry-II

In this post we will see the design of gable columns and gable wind girder or eave girder

 Gable Column:

Design of small industrial building with gantry-I

Design of  industrial building consists of the design of the following components.

This post deals with the design of the components starting from Gable rafter.

The factors governing the calculation of span length, dead load and wind load are given below

Dead Load : Roof sheeting @0.16 kN/m2, purlins @0.08 kN/m, self wt of gable rafter @ 0.1 kN/m
Live load of 0.5 kN/m2 can be assumed
Wind Load: IS 875-PartIII prescribes the value of C_pe as -0.8 as given below

Design moment: As mentioned in the figures above, the design moment can be taken as if gable rafter is simply supported between the columns. This is conservative and simplified approach.

Design moment capacity: Plastic moment capacity of a selected section can be obtained after locating the palstic neutral axis, as below

Design of Side rails/ Wall girts: 

Side rails suporting the wall sheeting are designed as laterally supported beams subjected to biaxial bending as prescribe in IS 800: 2007

Design loads are calculated based on the design values shown in the above figure. The external wind pressure coefficient is given below in IS 875-part III

Design moments in both directions can be obtained considering the continuous span to be simply supported between the columns

Design plastic moment capacities in both directions can be obtained directly from plastic section moduli given in IS 800-2007

The interaction formulae given below can be used to check this beam under biaxial bending

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