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**Sections**WORKSHEET 9a to answer just click on the button or image related to the answer let's go !!**moment of inertia**section modulus radius of gyration a b d c modulus of elasticity Question 1a what is the property of a beam’s X-section which affects its strength?**the depth**the width a b Question 1b what is the most important factor influencing the Section Modulus and thus the strength of a beam?**it feels like it should be**it is squared in the equation a b Question 1c why is the depth the most important factor in the section modulus?**modulus of elasticity**section modulus moment of inertia slenderness ratio a b d c Question 2a which property of a beam’s x-section affects a beam’s stiffness?**the breadth**the depth a b Question 2b which is the most important factor influencing the moment of inertia and thus the stiffness?**It seems to be**it is cubed in the equation a b Question 2c why is the depth the most important factor in the moment of inertia?**333.3 x 103 mm4**2.1 x 106 mm4 33.3 x 106 mm4 33.3 x 106 mm3 a b d c Question 3a a timber beam is 200 mm x 50 mm what is the moment of inertia of this beam?**83.3 x 103 mm3**333.3 x 103 mm4 333.3 x 103 mm3 a b c Question 3b a timber beam is 200 mm x 50 mm what is the section modulus of this beam?**83.3 x 103 mm4**166.7 x 103 mm3 8.3 x 106 mm4 a b c Question 4a a timber beam is 100 mm x 100 mm what is the moment of inertia of this beam?**8.3 x 106 mm4**166.7 x 103 mm3 166.7 x 103 mm4 a b c Question 4b a timber beam is 100 mm x 100 mm what is the section modulus of this beam?**b)**both the same weight a) a b c Question 5a given the two timber beam above, a) 200 x 50 mm and b) 100 x 100 mm which is the heavier?**b)**both the same stiffness a) a b c Question 5b • given the two timber beam above, • 200 x 50 mm (Ixx = 33.3 x 106 mm4; Zxx = 333.3 x 103 mm3); and • 100 x 100 mm (Ixx = 8.3 x 106 mm4; Zxx = 166.7 x 103 mm3) which is the stiffer about the X-X axis?**b)**both the same strength a) a b c Question 5c • given the two timber beams above, • 200 x 50 mm (Ixx = 33.3 x 106 mm4; Zxx = 333.3 x 103 mm3); and • 100 x 100 mm (Ixx = 8.3 x 106 mm4; Zxx = 166.7 x 103 mm3) which is the stronger about the X-X axis?**a beam should be deeper than wide**a beam should be wider than deep nothing a b c Question 6 • given the two timber beams above, • 200 x 50 mm (Ixx = 33.3 x 106 mm4; Zxx = 333.3 x 103 mm3); and • 100 x 100 mm (Ixx = 8.3 x 106 mm4; Zxx = 166.7 x 103 mm3) what have we learnt from the above?**125 mm**118 mm 200 mm a b c Question 7a we want a beam as stiff as a 200 x 50 mm (Ixx = 33.3 x 106 mm4) but we only have space for a 150 mm depth how wide must the beam be (theoretically)?**100 mm**103 mm 89 mm a b c Question 7b we want a beam as strong as a 200 x 50 mm (Zxx = 333.3 x 103 mm3) but we only have space for a 150 mm depth how wide must the beam be (theoretically)?**the width has to be increased a lot**the width has to be increased a bit nothing much a b c Question 7c when we reduce the depth of a beam a little what happens?**it may buckle**the depth may be a problem a no reason a and b b d c Question 8 if a beam should be as deep as possible why don’t we use an even deeper and narrower beam? e.g. a 300 x 20 mm beam**enough !**next question a Great Start**let me try again**let me out of here Sorry we are talking about strength**let me try again**let me out of here No Way !! the radius of gyration relates to columns**we are talking about the property of**a beam’s X-section NOT its material property let me try again let me out of here Think again !**I think you’ve got it**enough ! next question You Bewdy !**let me try again**let me out of here A devil of an answer !! you’re not trying**enough !**next question you've got it it!! since Z = bd2 / 6 if you double the depth, you quadruple Z**you’re not trying**let me try again let me out of here C'mon !**enough !**next question you've got it it!! 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**we are talking about the property of**a beam’s X-section NOT its material property let me try again let me out of here Oh my gosh!!**didn’t we just decide that**the Section Modulus affects the strength? let me try again let me out of here Oh my gosh!!**the slenderness ratio relates to**columns not beams let me try again let me out of here Oh my gosh!!**enough !**next question Fantastic You’ve got it !**you mustn’t be trying !**let me try again let me out of here This is really sad**enough !**next question Yeaaahh! since I = bd3 / 12 if you double the depth, I increases by a factor of 8**you’re not trying**let me try again let me out of here C'mon !**enough !**next question terriffic !! I = bd3 / 12 I = 50 x 2003 / 12 I = 50 x 8 x 106 / 12 I = 33.3 x 106 mm4**let me try again**let me out of here it's enough to make one cry What is the depth? What is the width? Didn’t we say that a beam has to be deeper than wide?**be more careful with your zeros !**let me try again let me out of here Not right !**let me try again**let me out of here it's enough to make one cry what are the units for I? the formula for I is bd3 / 12 so that’s mm x mm3**enough !**next question Yipee !! you’ve got it !! Z = bd2 / 6 Z = 50 x 2002 / 6 Z = 50 x 4 x 104 / 6 Z = 333.3 x 103 mm3**let me try again**let me out of here it's enough to make one cry What is the depth? What is the width? Didn’t we say that a beam has to be deeper than wide?**let me try again**let me out of here it's enough to make one cry what are the units for Z? the formula for I is bd2 / 16 so that’s mm x mm2**enough !**next question terriffic !! I = bd3 / 12 I = 100 x 1003 / 12 I = 100 x 106 / 12 I = 33.3 x 106 mm4**be more careful with your calculation !**let me try again let me out of here Not right ! what are the units for I? the formula for I is bd3 / 12 so that’s mm x mm3**be more careful with your zeros !**let me try again let me out of here Not right !**enough !**next question Yipee !! you’ve got it !! Z = bd2 / 6 Z = 100 x 1002 / 6 Z = 1000 x 103 / 6 Z = 166.7 x 103 mm3**be more careful with your calculation !**let me try again let me out of here it's enough to make one cry what are the units for I? the formula for I is bd3 / 12 so that’s mm x mm3**next question**enough ! Yipee !! Yes! Both have the same X-sectional area So must have the same amount of material and weigh the same**let me try again**let me out of here Think again ! What is the X-sectional area of a? What is the X-sectional area of b)?**enough !**next question yes, yes, yes !! brilliant Since the Moment of Inertia of a) is 33.3 x 106 mm4 while the Moment of Inertia of b) is 8.3 x 106 mm4 beam a) is ~4 times stiffer than beam b)