Ultimate load states
The ultimate limit state design is based on rules given in EN 1996-1-1, chapter 6.
Unreinforced masonry walls subjected to mainly vertical loading
Basic equation for design of unreinforced masonry walls subjected to mainly vertical loading is (in accordance with paragraph 6.1.2):
where: | NEd |
|
NRd |
|
The design value of the vertical resistance NRd is calculated using formula
where: | Φ |
|
A |
| |
fd |
|
The design compressive strength fd of the cross-sections with area smaller than 0.1m2 is multiplied in accordance with 6.1.2.1.(3) by factor
kde je: | A |
|
The calculation of reduction factor for slenderness and eccentricity Φi at the top and bottom of the wall is based on on a rectangular stress block:
where: | Φi |
|
ei |
| |
t |
|
The eccentricity at the top or bottom of the wall ei is calculated using equation
where: | Mid |
|
Nid |
| |
einit |
| |
t |
|
The initial eccentricity is calculated in accordance with 5.5.1.1(4) using equation
where: | hef |
|
The reduction factor within the middle height of the wall Φm is calculated according to the annex G. Following equation is used for the walls with rectagular cross-sections:
where is
and
where is
The eccentricity at the middle height of the wall emk is calculated using equation
where: | em |
|
ek |
| |
t |
|
The eccentricity due to loads em is calculated using equation
where: | Mmd |
|
Nmd |
| |
einit |
|
The eccentricity due to creep ek is calculated using equation
where: | hef |
|
tef |
| |
Φ∞ |
| |
t |
| |
em |
|
For walls fulfilling condition
is the eccentricity due to creep ek equal to zero.
The design value of the vertical force is calculated using iteration of the deformation along the cross-section area under conditions written in 6.1.1(2) for more complicated shapes of the cross-sections. the stress-strain relationship diagram is taken to be rectangular. Normal force can't be equal to zero and can't be located outside the cross-section.
Unreinforced masonry walls subjected to lateral loading
Basic equation for design of unreinforced masonry walls subjected to lateral loading is (in accordance with paragraph 6.3.1):
where: | MEd |
|
MRd |
|
The design value of the bending resistance MRd is calculated using equation
where: | fxd |
|
Z |
|
When a vertical load is present, the favourable effect of the vertical stress is considered using equation in accordance with 6.3.1(4)(i):
where: | fxd |
|
σd |
|
Unreinforced masonry walls subjected to shear loading
Shear is analysed according to 6.2, basic equation is
where: | VEd |
|
VRd |
|
The design value of the shear resistance MRd is calculated using equation
where: | VRd |
|
fvd |
| |
Ac |
|
Buckling of columns with more complicated cross-sections
Buckling verification of columns, that have more complicated shapes of cross-sections, is performed with the help of an effective cross-section. The effective cross-section is a rectangle, that is selected according to the following rules:
- The area of the effective cross-section is identical to the area of the real cross-section
- The ratio Wy/Wz is identical for the real and effective cross-sections
Walls subjected to concentrated loads
Basic equation for design of walls subjected to concentrated vertical load (in accordance with paragraph 6.1.3):
where: | NEdc |
|
NRdc |
|
Design value of the vertical concentrated load resistance NRdc is calculated using equation:
where: | β |
|
Ab |
| |
fd |
|
Enhancement factor for concentrated load β is calculated using equation:
where: | a1 |
|
hc |
| |
Aef |
| |
lefm |
|