Portal Frame Analysis Using Excel

INTRODUCTION

The strength checks for any structure are valid only if the analysis gives a good representation of the behavior of the actual structure. Basically, the structural form can be analyse by using portal frame method which is an approximate analysis for the structural building frames subjected to lateral loading. Let say for a building frames which have height is less than width, this method is more suitable for the analysis since it a low rise condition.There are a few type of portal frames which is use in building such as portal support, concrete portal, masonry portals, and steel portal as shown in Figure 1.

Figure 1: Steel Portal Frames

 Source: www.rexbarnesengineering.co.nz

In general understanding, when any frame is loaded, it deflects and its shape under load is different form the un-deformed shape. The deflection will causes the axial loads in the members to act along different lines. If the deflections are small, the consequences are very small and a first order analysis (by set assumption: neglecting the effects of the deflected shape) is sufficiently accurate. However, in case of deflections are such that the effects of the axial load on the deflected share are large enough to cause significant additional moment and further deflection, second order analysis is sufficiently accurate which reduce the resistance of the frame since the portal frame is said to be sensitive to the second order effect.

Other than that, portal frames mainly consist of 2D rigid frames (column and beams) which rigidly joint together. The basic design can be understand easily as long as we understand the fundamental of portal frames. Nowadays, too many design of structure involve in complex design and require complex analysis which necessarily applying the fundamental knowledge where the understanding of the portal frame behavior towards a stable structure is required.

OBJECTIVE

Basically for this study, the objective is to understand the portal frames behavior and how bending moment in the beam be reduce, which allows the frame to act as one single structural unit. Below are the objective for this analysis:

1. To determine experimental values for the deflections of a portal frame and compare these with the Frame2D excel method.
2. To determine the experimental values of the reactions and compare them with Frame2D excel method

APPARATUS

Bending Moment Portal frames, ruler and loads

EXPERIMENT

                                 Figure 2: Bending moment portal frames equipment

In this study, few assumption is set in order to makes the experiment and analysis much easier to construct. We assume:

1. No moment exist at the applied load boundary because of two roller support is used
2. Young modulus is 200000 N/mm^2.

EXPERIMENTAL RESULTS

TABLE 1: Displacement result form experimental method

 FINITE ELEMENT ANALYSIS METHOD (FEA)

For this finite element analysis method, the portal frames is modeled. The applied force is at horizontal axis and the displacement at the x-axis is collected. The basic input loading, geometry, material and boundary condition is set in excel method. Based on Figure 3 and Figure 4, the portal frames is modeled as 610 mm height and 600 mm wide with the 10 mm x 25 mm cross section area.  Figure 3 is been analyse by set 3 element while for the Figure 4 the element is 6.

Calculation

FEA

Figure 3: Two Dimensional model of portal frame with 3 element

Figure 4: Two- Dimensional model of portal frame with 6 element

To solve this portal frame problem, excel file FRAME2D is used. Based on Figure 5 and 6 the area and moment inertia is set as per calculated above, and the rest is set based on the model designed.

  Figure 5: Solving by apply 3 Element

             

Figure 6: Solving by apply 6 element

Based on Figure 5 and 6, the red circle represent area, inertia and load set up respectively. This step is repeated by replace the load as 5N, 7N and 9N. The load is key in as negative based on the Figure 3 and 4 which load applied is toward left side which assume as negative applied load. For Figure 5 and 6, Nodes 1  set to be fixed support with no displacement or deformation occur. While for the Node 4 in Figure 5 where horizontal load applied to it which will have a deformation on Q10 and Q12 while for Q11, the vertical direction is assumed to have no deformation. Same as Figure 6 where 6 element is apply, the Node 7 will have deformation on Q19 and Q21.

Figure 7: Result of Displacement on x-axis for 3 element

Figure 8: Result of Displacement on x-axis for 6 element

The step on Figure 5 and 6 is repeat and the data result is collected as Table 2 and percentage error also calculated to know which is the most appropriate either using 3 element or 6 element.

Table 2: Result from excel file FRAME 2D for 3 and 6 element

Based on Table 2, we can plot a graph of force against displacement which compare the experimental and finite element analysis (3 & 6 element). Table 2 shows the percentage error that have been calculated, which can be elaborate that by divide the model designed into 6 division of element, the error is less as compared to 3 division element. This may conclude as the 6 division of element is more appropriate to use in this modelling for portal frame.

Based on the graph above, it shows that the 6 division of element is much more near to the experimental result compared to 3 division of element. On the other hand, the relationship that can be relate based on this grapg is, as the load applied is increase, the displacement is increasing. However, this graph shows the slightly different result for experimental and analysis since the percentage error is increase as the load applied increase until up to 19%. This occur maybe due to a few error while conducting the experiment and parameter set up in excel files was not the exact value.