By J. D. Todd (auth.)
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Extra resources for Structural Theory and Analysis
The value of R2 will be increased while that of R I stays constant. Thus the inequality will not be affected by a load coming onto the beam. The same kind of argument will apply if PI leaves the beam. If however P 3 reaches and crosses C the value of R I will increase suddenly and that of R2 will decrease and the inequality may no longer be true. We can now see that the maximum bending moment will occur when one of the loads is at the point C. 18) may be used to determine which load will give the maximum value.
With the loads continuing to move to the right the value of the positive shear force will again increase while that of the negative shear force due to PI will decrease. This state of affairs will continue until 36 STRUCTURAL THEORY AND ANALYSIS P2 is just to the left of C, and the net shear force can be found. It can now be seen that the maximum value of the positive shear will occur when one of the point loads is just to the left of C. It also follows that the maximum value of negative shear will occur when one of the loads is just to the right of C.
The area and centroid of each strip can be found. The area will represent a small load which can be considered as acting through the centroid. The force and funicular polygon can be drawn, the latter will have to be slightly corrected by making the rays tangential to a curve, which can be drawn freehand. 5. To solve the problem graphically it is necessary to consider the loads on each half of the arch separately. 26b shows it with the loads on the right-hand side removed. Considering this second case, the direction of the reaction R B must pass through the points Band C as the 26 STRUCTURAL THEORY AND ANALYSIS t ~ c / R.