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Strength of Materials - Lecture Notes / Mehmet Zor

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9. Deflection of Beams

 

(ELASTIC CURVE)

9.1 General Informations

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Strength of Materials - Lecture Notes / Mehmet Zor

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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:

  1. The beam section is symmetrical with respect to at least one of the y or z axes.
  2. Only internal moment Mz occurs in beam sections (for this reason, the beam is exposed to loads in the x-y plane).

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

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Strength of Materials - Lecture Notes / Mehmet Zor

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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

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Strength of Materials - Lecture Notes / Mehmet Zor

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9.1.4 Methods for Calculating Deflection and Slope:

  1. Analytical method (integration method) 9.2
  2. Moment Area Method 9.3
  3. Conjugate Beam Method 9.4
  4. Superposition Method and Hyperstatic Systems 9.5
  5. Energy Methods and Castigliano Theorems 10.1, 10.2

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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