AS3700 unreinforced masonry in horizontal bending 1

[CZHOU]

hi all, I'm wondering if anyone is familiar with the Australian Standard 3700, in particular section section 7.4.3 - design of member in horizontal bending.

the design criteria is Mdh < Mch,
where Mdh = design horizontal bending moment resulting from transient out-of-plane forces acting on a wall in a horizontal-spanning action
Mch = horizontal bending moment capacity in N.mm per metre length of wall

the code then gives 3 equations to evaluate Mch, based on 2 failure modes - line failure and stepped failure.

The equations are functions of Zd, Zu and Zp, where:
Zd = section modulus of the bedded area, in mm^3/m length
Zu = lateral section modulus of masonry units, in mm^3/m length
Zp = lateral section modulus of the mortar contact area of the perpend joints, in mm^3/m length

my questions:
1. why is Mch, the moment capacity, in units of N.mm per metre length of wall? Does that mean a longer wall is stronger in bending?
2. I'm not sure how to calculate Zd, Zu and Zp. I know the sectio modulus is bh^2/6 for a rectangular section, but I'm not sure what to take for b & h in each case.
3. why are the section modulus in units of mm^3 / m length? shouldn't it be mm^3?

I'd really appreciate a pointer as to where I might get the answer. thanks in advance!

 

[Harste]

Hello,

My responses are below, but I would strongly recommend taking a look at the Think Brick technical manuals, particularly TBA04:

http://thinkbrick.com.au/technical

They have explanations and worked examples to AS3700 which you can follow.

1. I agree that the wording is somewhat misleading. This calculation is for one-way bending of a masonry wall. Mdh should be your moment per meter width, taking into account the length of wall between your supports. Mch is a section modulus, Zd, calculated using a 1m wide wall cross-section.

2. As I said in (1), the Z calculations are for a section modulus for a 1m wide cross-section of wall. b would be 1000mm, h would be the masonry unit thickness (wall thickness).

3. Most calculations in AS3700 are per meter calculations. Following (2) will give a Z value in mm^3 for a 1m wide cross-section of wall, hence mm^3/m.

AS3700 constantly changes what the word 'length' means, depending on whether you're considering vertical or horizontal bending. To me, length is always be the wall length between supports for one-way bending. For vertical bending, 'width' is a horizontal measurement. For horizontal bending, 'width' is a vertical measurement (or the 'height' of your wall).

Hope this helps.

 

[Retrograde]

There are some good worked examples, as well as design charts, here:

https://www.nationalmasonry.com.au/wp-content/uploads/CMAA-Horizontal-Loads.pdf

 

[CZHOU]

thank you Retrograde & Harste for your help! I shall read these references thoroughly!