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Sections WORKSHEET 9a to answer just click on the button or image related to the answer

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Question 1a moment of inertia a section modulus b radius of gyration c what is the property of a beam’s X-section which affects its strength? modulus of elasticity d

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Question 1b the depth a the width b what is the most important factor influencing the Section Modulus and thus the strength of a beam?

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Question 1c it feels like it should be a it is squared in the equation b why is the depth the most important factor in the section modulus?

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Question 2a modulus of elasticity a section modulus b moment of inertia c which property of a beam’s x-section affects a beam’s stiffness? slenderness ratio d

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Question 2b the breadth a the depth b which is the most important factor influencing the moment of inertia and thus the stiffness?

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Question 2c It seems to be a it is cubed in the equation b why is the depth the most important factor in the moment of inertia?

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Question 3a a timber beam is 200 mm x 50 mm 2.1 x 10 6 mm 4 a x 10 3 mm 4 b 33.3 x 10 6 mm 4 c what is the moment of inertia of this beam? 33.3 x 10 6 mm 3 d

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a timber beam is 200 mm x 50 mm Question 3b x 10 3 mm 3 a 83.3 x 10 3 mm 3 b x 10 3 mm 4 c what is the section modulus of this beam?

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Question 4a a timber beam is 100 mm x 100 mm x 10 3 mm 3 a 83.3 x 10 3 mm 4 b 8.3 x 10 6 mm 4 c what is the moment of inertia of this beam?

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Question 4b a timber beam is 100 mm x 100 mm x 10 3 mm 4 a 8.3 x 10 6 mm 4 b x 10 3 mm 3 c what is the section modulus of this beam?

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Question 5a given the two timber beam above, a) 200 x 50 mm and b) 100 x 100 mm a) a b) b both the same weight c which is the heavier?

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Question 5b given the two timber beam above, a)200 x 50 mm (I xx = 33.3 x 10 6 mm 4 ; Z xx = x 10 3 mm 3 ); and b)100 x 100 mm (I xx = 8.3 x 10 6 mm 4 ; Z xx = x 10 3 mm 3 ) a) a b) b both the same stiffness c which is the stiffer about the X-X axis?

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Question 5c given the two timber beams above, a)200 x 50 mm (I xx = 33.3 x 10 6 mm 4 ; Z xx = x 10 3 mm 3 ); and b)100 x 100 mm (I xx = 8.3 x 10 6 mm 4 ; Z xx = x 10 3 mm 3 ) a) a b) b both the same strength c which is the stronger about the X-X axis?

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Question 6 given the two timber beams above, a)200 x 50 mm (I xx = 33.3 x 10 6 mm 4 ; Z xx = x 10 3 mm 3 ); and b)100 x 100 mm (I xx = 8.3 x 10 6 mm 4 ; Z xx = x 10 3 mm 3 ) nothing a a beam should be deeper than wide b what have we learnt from the above? a beam should be wider than deep c

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Question 7a we want a beam as stiff as a 200 x 50 mm (I xx = 33.3 x 10 6 mm 4 ) but we only have space for a 150 mm depth 200 mm a 125 mm b 118 mm c how wide must the beam be (theoretically)?

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Question 7b we want a beam as strong as a 200 x 50 mm (Z xx = x 10 3 mm 3 ) but we only have space for a 150 mm depth 89 mm a 100 mm b 103 mm c how wide must the beam be (theoretically)?

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Question 7c when we reduce the depth of a beam a little nothing much a the width has to be increased a lot b the width has to be increased a bit c what happens?

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Question 8 if a beam should be as deep as possible the depth may be a problem a it may buckle b no reason c why don’t we use an even deeper and narrower beam? e.g. a 300 x 20 mm beam a and b d

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next question enough !

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let me try again let me out of here we are talking about strength

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let me try again let me out of here the radius of gyration relates to columns

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let me try again let me out of here we are talking about the property of a beam’s X-section NOT its material property

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next question enough ! I think you’ve got it

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let me try again let me out of here you’re not trying

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next question enough ! since Z = bd 2 / 6 if you double the depth, you quadruple Z

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let me try again let me out of here you’re not trying

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next question enough ! the Moment of Inertia figures in the deflection formula D = k x WL3 / EI (k is a constant depending on the type of beam support and loading) so the greater the value of I, the smaller the deflection of the beam

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let me try again let me out of here we are talking about the property of a beam’s X-section NOT its material property

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let me try again let me out of here didn’t we just decide that the Section Modulus affects the strength?

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let me try again let me out of here the slenderness ratio relates to columns not beams

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next question enough ! You’ve got it !

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let me try again let me out of here you mustn’t be trying !

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next question enough ! since I = bd 3 / 12 if you double the depth, I increases by a factor of 8

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let me try again let me out of here you’re not trying

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next question enough ! I = bd 3 / 12 I = 50 x / 12 I = 50 x 8 x 10 6 / 12 I = 33.3 x 10 6 mm 4

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let me try again let me out of here What is the depth? What is the width? Didn’t we say that a beam has to be deeper than wide?

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let me try again let me out of here be more careful with your zeros !

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let me try again let me out of here what are the units for I? the formula for I is bd 3 / 12 so that’s mm x mm 3

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next question enough ! you’ve got it !! Z = bd 2 / 6 Z = 50 x / 6 Z = 50 x 4 x 10 4 / 6 Z = x 10 3 mm 3

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let me try again let me out of here What is the depth? What is the width? Didn’t we say that a beam has to be deeper than wide?

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let me try again let me out of here what are the units for Z? the formula for I is bd 2 / 16 so that’s mm x mm 2

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next question enough ! I = bd 3 / 12 I = 100 x / 12 I = 100 x 10 6 / 12 I = 33.3 x 10 6 mm 4

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let me try again let me out of here be more careful with your calculation ! what are the units for I? the formula for I is bd 3 / 12 so that’s mm x mm 3

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let me try again let me out of here be more careful with your zeros !

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next question enough ! you’ve got it !! Z = bd 2 / 6 Z = 100 x / 6 Z = 1000 x 10 3 / 6 Z = x 10 3 mm 3

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let me try again let me out of here be more careful with your calculation ! what are the units for I? the formula for I is bd 3 / 12 so that’s mm x mm 3

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next question enough ! Yes! Both have the same X-sectional area So must have the same amount of material and weigh the same

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let me try again let me out of here What is the X-sectional area of a? What is the X-sectional area of b)?

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next question enough ! brilliant Since the Moment of Inertia of a) is 33.3 x 10 6 mm 4 while the Moment of Inertia of b) is 8.3 x 10 6 mm 4 beam a) is ~4 times stiffer than beam b)

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let me try again let me out of here Don’t guess What is the Moment of Inertia of a)? What is the Moment of Inertia of b)?

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next question enough ! You’ve got it! Since the Section Modulus of a) is x 10 3 mm 3 while the Section Modulus of b) is x 10 3 mm 3 beam a) is twice as stiff as beam b)

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let me try again let me out of here Don’t guess What is the Section Modulus of a)? What is the Section Modulus of b)?

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next question enough ! You’ve got it in one! Let’s just keep remembering A beam should be deeper than wide … A beam should be deeper …………….

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let me try again let me out of here you’re not trying You must have learnt something!

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let me try again let me out of here after everything that we have done You can say that!

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next question enough ! I x = 33.3 x 10 6 mm 4 I x = bd 3 / x 10 6 = b x /12 b = 33.3 x 10 6 / (150 3 /12) b = 118 mm

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let me try again let me out of here think it through You know the depth you can have What do you know about the Moment of Inertia?

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next question enough ! Z x = x 10 3 mm 3 Z x = bd 2 / x 10 3 = b x /6 b = x 10 3 / (150 2 /6) b = 89 mm

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let me try again let me out of here think it through You know the depth you can have What do you know about the Section Modulus?

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next question enough ! You really understand it now!

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let me try again let me out of here You are joking (aren’t you?)

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let me try again let me out of here 50 89 Is that a bit?

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You’ve graduated with honours! FINISH Yes there is a limit to how thin and deep we can make a beam When loaded, the web is in compression and so may buckle

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let me try again let me out of here That’s part of the answer

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let me try again let me out of here Try thinking !

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