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Qualitative Influence Lines




In 1886, Heinrich Müller-Breslau developed a technique for rapidly constructing the shape of an influence line. Referred to as the Müller-Breslau the principle, the principle stating that the shape of influence line for a function of reaction, shear, or moment is the same shape of the beam deflection when the beam is subjected to function of reaction, shear, or moment. In order to draw the deflection shape of the beam. The capacity of the beam to resist the acted function shall be removed. For example, if the influence line is required for the vertical reaction at point A in a beam where point A is a pin. The pin will be replaced with a roller to remove the resistance for a vertical reaction while keeping resistance for horizontal forces. The figure no:1-a showing a beam, if the influence line for the vertical reaction to be determined at point A. as I said before, the pin will be replaced with a  guided roller to eliminate the resistance to vertical reaction and to allow the beam to deflect so we can draw Qualitative Influence Line for the beam. When a positive force Ay is applied at point A, the beam will deflect to the dashed shape shown in figure no:1-b. The deflection of the beam represents a qualitative influence line for the beam.

Figure 1


Let draw the influence line for shear at point C for the beam shown in figure no:2-a. To draw the shear for influence line, we should eliminate the beam resistance for shear at point C so we can draw the deflection shape of the beam. We will place a roller at point C, as shown in figure no:2-b. The deflection of the beam will be as shown in figure no:2-b. If we need to draw the influence line for the moment at point C., we should place an internal hinge at this point to eliminate the beam resistance to the moment. The deflection of the beam due to moment at point C will be as shown in figure no:3-b. The deflection of the beam will represent the influence line for the moment at point C, as I mentioned before.


Figure 2

Figure 3


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