Sections

1. Sections WORKSHEET 9a to answer just click on the button or image related to the answer let's go !!

2. 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?

3. 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?

4. 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?

5. 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?

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

7. 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?

8. 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?

9. 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?

10. 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?

11. 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?

12. 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?

13. 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?

14. 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?

15. 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?

16. 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)?

17. 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)?

18. 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?

19. 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

20. enough ! next question a Great Start

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

22. let me try again let me out of here No Way !! the radius of gyration relates to columns

23. 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 !

24. I think you’ve got it enough ! next question You Bewdy !

25. let me try again let me out of here A devil of an answer !! you’re not trying

26. enough ! next question you've got it it!! since Z = bd2 / 6 if you double the depth, you quadruple Z

27. you’re not trying let me try again let me out of here C'mon !

28. 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

29. 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!!

30. didn’t we just decide that the Section Modulus affects the strength? let me try again let me out of here Oh my gosh!!

31. the slenderness ratio relates to columns not beams let me try again let me out of here Oh my gosh!!

32. enough ! next question Fantastic You’ve got it !

33. you mustn’t be trying ! let me try again let me out of here This is really sad

34. enough ! next question Yeaaahh! since I = bd3 / 12 if you double the depth, I increases by a factor of 8

35. you’re not trying let me try again let me out of here C'mon !

36. 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

37. 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?

38. be more careful with your zeros ! let me try again let me out of here Not right !

39. 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

40. 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

41. 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?

42. 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

43. enough ! next question terriffic !! I = bd3 / 12 I = 100 x 1003 / 12 I = 100 x 106 / 12 I = 33.3 x 106 mm4

44. 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

45. be more careful with your zeros ! let me try again let me out of here Not right !

46. 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

47. 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

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

49. 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)?

50. 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)