Structural Design Theories

7/30/2019 Structural Design Theories

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Statically Determinate Beams


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SF & BM Diagrams - Single Concentrated Load


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SF & BM Diagrams - Uniformly Distributed Load


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Calculation of the Second Moment of Area I

Item Area =A y A.y h A.h A.h2 INA

1 44 x 6 264 97 25608 36.87 9734 358880 790

2 25 x 6 150 87.5 13125 27.37 4106 112370 7810

3 47 x 3 141 1.5 212 58.63 8267 484680 100

4 25 x 3 75 12.5 938 47.63 3572 170150 3900

5 86 x 2 172 48.5 8342 11.63 2000 23260 106000

SUM 802 48225 1149340 118600


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Effective Bending Section - Buckled Web


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Stresses Due to Bending Moment

Figure 5/6a


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Stresses Due to Bending Plus End Load

Figure 5/6b

Eff i D h f B


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Effective Depth of Beam

BM = 8 KNm

Couple P = 8/91 = 87.9 KN

Area of Compression Flange = 44 x 6 + 16 x 8 = 392 mm2

Area of Tension Flange = 47 x 3 + 16 x 5 = 221 mm2

I iti l E ti t f L d i St i


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Initial Estimate of Loads in Stringers

D fl ti f C til ith


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Deflection of Cantilever withConcentrated Load at Tip

Deflection of Simply Supported Beam


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Deflection of Simply Supported Beamwith Uniformly Distributed Load

Example Beam Deflection


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Example - Beam Deflection

Calculate the maximum deflection at the centre-line

and weight of the top and bottom skins

E = 110000 N/mm2 (Titanium)

Allowable stress - Top = 675 N/mm2

B 750 N/ 2

Tornado Carry through Box


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Tornado Carry-through Box

Plastic Bending


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Plastic Bending

Allowable Moment - Plastic & Elastic Bending


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Allowable Moment - Plastic & Elastic Bending


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Plastic Bending - Assumed Stress Distribution


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Plastic Bending Assumed Stress Distribution

Statically Determinate &


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Statically Determinate &Statically Indeterminate Structures

Strain Energy in Tension


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St a e gy e s o

Example 1 - Strain Energy - Propped Cantilever


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p gy pp

Example 2 - Strain Energy - Beam on 3 Supports


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p gy pp

Deflection of a Cantilever Beam


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Deflection of a Simply Supported Beam


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Determine maximum deflection at centre of beam

E = 72000 N/mm2 I = 1.2 x 106 mm4

Using Castiglianos Theorem

Apply load P at centre of beam

Theorem of Three Moments


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Example of Theorem of Three Moments


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Example - Theorem of Three Moments


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For the above beam, draw the BM and SF diagrams

Use the theorem of three moments

Assume EI are constant

FIGURE5/24

Shear Stress Distribution - Rectangular Section


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Shear Stress Distribution - I beams


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Shear Stress Distribution inFl f Ch l & I S ti


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Flanges of Channel & I Section

Complementary Shear Stress


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Web Shear Flows


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Example Shear Flows & End Loads


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FIGURE5/30

Calculate the shear flow in the web and the load distribution in the members

Structural Design Theories

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