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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