Strength of Materials - Lecture Notes / Mehmet Zor
1
23 Agust 2024
9. Deflection of Beams
(ELASTIC CURVE)
9.1 General Informations
Strength of Materials - Lecture Notes / Mehmet Zor
2
23 Agust 2024
The form taken by a beam subjected to loads in the x-y plane and especially in the vertical direction, changing shape within elastic limits, is called an elastic curve.
9.1.2 In order to meet the Simple Bending condition, we will only examine systems that have the following 2 features:
Deflection of Beams
Elastic Curve
Original beam axis
ν
Figure 9.1.1
Figure 9.1.2
Figure 9.1.3
Elastic Curve
9.1 General information
Strength of Materials - Lecture Notes / Mehmet Zor
3
23 Agust 2024
In the design of beams, not only stresses but also deflections are of great importance.
9.1.3 The Importance of Deflection Calculation in Beams
L
P1
P2
P3
vmax
Therefore, the ratio of maximum deflection to beam length (vmax/L) is not desired to exceed a certain value (1/300).
Deflection of Beams
Figure 9.1.4
Figure 9.e
In Russia, a suspension bridge over a river partially collapsed while a pickup truck was passing over it. Those moments were captured on camera as the vehicle sank into the water.
The incident took place in the village of Uyum, 4,500 kilometers away from Moscow. The wooden suspension bridge over the river could not bear the weight of the truck passing over it and partially collapsed. While it was reported that the driver of the vehicle was rescued after the accident, it was reported that the truck could not be removed from the water.
NEWS
Figure 9.1.5
Strength of Materials - Lecture Notes / Mehmet Zor
4
23 Agust 2024
9.1.4 Methods for Calculating Deflection and Slope:
Here the first 4 methods will be explained with examples.
The 5th topic, energy methods, will be shown later.
Deflection of Beams
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