Z Reference

Anyone please advise on what Z is in the equation? thanks.

Z is the section modulus. It is equal to where

• I is the second moment of inertia
• y is the distance between the axes of I and Z.

Z is usually calculated on the surface of a beam, so for a rectangular box, y=half its height.

(I think the pages need updating to explain this.)

Hey

Can you confirm this please?

Z = I / y

I = BD^3 / 12

Y-rectange = d / 2

Y is described as the distance from the neutral axis, but distance to where? top or bottom?

Can this be calculated as

Z = BD^2 / 6 ?????

Thanks for any more light you can shed on this.

I also want to add that this site is one of the best, if not the best resource i have came upon whilst studying Mechanical Engineering, its excellent, and i will be passing the link on to fellow students and lectureres.

Hi

I entered the original reference page and I would have answered your query earlier but my Broadband went down yet again!

I am sure you know the equation well neglect the right hand fraction and re-arrange the other two so:-

If you look at this equation you can see that for any given cross section y mas a maximum value as it is the distance from the Neutral Axis to the "outside" of the section. Likewise I is a Constant for that section being bent in that plane. Hence I can re-write the above equation as:-

Actually it might be better to write this as:-

M in this equation is the Maximum Bending moment that can be carried by the given section for a given maximum Stress. It is called the Moment of Resistance

Now look at your Post of the 20Th Nov.

Y is actually the distance from the neutral axis to where ever you want to know the stress. Of course this is usually the "outside" of the section because that is where the stress is a maximum. You ask whether you should measure upwards or downwards. Well that depends upon what you want. On a simply supported beam subjected to a downwards load the upper surfaces goes into Compression and the lower Tension and the important one depends upon the relative maximum compressive and Tensile stresses.

You asked about a rectangular section and the neutral axis is central. Had it been a "T" cross section the neutral axis would no longer be central and its position would need to be calculated.

In the particular example you gave you are correct. I hope that I have sorted out your problems.

Hey

Sorted them out, and thanks for that additional info.

I am now trying to figure out how to calculate using two loading points on a fixed end beam and having little, well no luck. From reading i can see that maybe you would use superpossition, but not 100% sure.

I am trying to figure out the Macaulay Method too, but because my maths isnt that good i am making no progress their. Rather than give up, it be good if some one can identify the maths required to solve so i can learn them .

thanks

Hi

May I suggest that you study example 3 in "The Bending Of Beams Part 5" The beam in the example is both built in and carries two loads. However it also carries a uniform load which you will have to remove!

I am afraid that you will have to learn some Mathematics if you want to be an engineer. As a help we have some useful pages on Integration; Differential equations. Trigonometry and Coordinate (Analytical) Geometry. They all have worked examples which should help you

I do not understand why the modular ratio m is introduced in the reaction loads in the case of the 'Continuous Beam With Two Unequal Spans With Two Unequal Loads At Any Point On Each'.

In the section 'Fixed at both ends. Load at any point', the deflection at the load is given as y = Wa^3b^2/6EIL^3. However, where load is in the centre, i.e. subsituting a = L/2 and b = L/2, the load deflection in the equation becomes:

W = W(0.5L)^3(L - 0.5L)^2/6EIL^3

= WL^3L^2/192EIL^3

= WL^5/192EIL^3

= WL^2/192EI

which is not correct, because it should be WL^3/192EI