The graph shows there is a direct, linear relationship between the maximum load applied

to the apex of the A-frame models and their H/S ratios.  This is due to the fact that the

greater the H/S ratio the more parallel the legs of the A-frame are to the downward vertical

force of the load and the upward force of the reactions at the base.  And the more the

legs are aligned with these forces the less compressive stresses are induced in the legs

and the less tensile stresses are induced in the base of the A-frame.  Thus the tall, narrow

IT A-frame model carried a heavier maximum load at the point of failure than the shorter,

wider RT model.   The weakest links in the structure were the joints joining the legs to the

base which failed due to excess tensile stresses.  The following figure shows the estimated
compressive (red) and tensile (blue) stresses induced in the RT and IT models by the actual

test loads.  Notice that although the IT A-frame withstood a maximum load that was nearly

 

    

Figure  158

Estimated compressive

and tensile stresses in

A-frame models with

different H/S ratios

 

 

two and one-half times the load of the RT structure, the estimated tensile stresses

experienced by their base members were about the same.   This verifies the destructive

testing results of the models.

 

Note:  Gaining a deeper understanding of the forgoing empirical observations involves

doing a static analysis of the A-frame structure. This has to do with how forces and reactions

are quantified and added together as vectors.  You are encouraged to click here to see how

this is done.

.

Exercise: 1)  Construct four A-frame models like those shown in Fig. 157.   Examine their

                     load bearing characteristics when a) the base tie member is a rubber band,

                     and b) when the base is a panel. Push down on the apex to test their strength.

                2)  Do destructive testing of the models built in 1b).  Graph and compare your

                     results.

                3)  Advanced - Test the holding strength of the pinge joint used in the A-frame

                     models.  Use this value to predict the maximum load the models should be

                     able to bear based on a static analysis.  Compare your results to the test data.

                4)  Advanced -  Using the load test results from 2) compute the maximum tensile

                     stress experienced by the base member at the point of failure using static

                     analysis.  Compare this value with the actual test data of 3).

.

Since longer spans require the A-frame truss of the Kingpost bridge to be taller, there is a

limit to the distance it can span before the legs of the truss get too tall, heavy, and costly.

.

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Page 102 - Building stability - A-frame structure

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