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

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

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?

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?

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

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

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?

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

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?

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?

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?

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?

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?

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?

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

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)?

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)?

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?

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

next question enough !

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

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

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

next question enough ! I think you’ve got it

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

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

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

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

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

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

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

next question enough ! You’ve got it !

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

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

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

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

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?

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

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

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

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?

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

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

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

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

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

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

next question enough ! 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 What is the X-sectional area of a? What is the X-sectional area of b)?

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)

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)?

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)

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)?

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 …………….

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

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

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

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?

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

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?

next question enough ! You really understand it now!

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

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

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

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

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