I'm trying to understand how ACI 530 address second order effects for members subject to axial and bending forces.
Here is what I find in the code:
I will use eqn numbers from 318-05 but the concept appears to be the same up through the 2013 code.
I see that for unreinforced masonry there are the following capacity equations:
1. (2) equations for allowable axial stress (one if h/r<99 (2-12) and one if h/r >99 (2-13)).
2. Then the P<1/4*Pe check. (eqn 2-11)
The commentary states that at larger h/r values where moment magnification is more critical the allowable axial load is limited by equation 2-11. The commentary then explains that Pe is a check to safeguard against premature buckling with loads applied at large eccentricities. It also states that ‘e’ is the actual eccentricity not the ‘virtual eccentricity’ caused by M/P where M is due to other loadings i.e. lateral loads. Therefore it seems that eqn 2-11 eliminates stability concerns in slender sections related to secondary moments for unreinforced sections.
For reinforced masonry there are the following criteria:
1. (2) equations for axial capacity. (2-17 and 2-18)
2. Combined compressive stress must be less than f’m/3
3. Axial component (only) must be less that Fa (which are the 2 equations found in the unreinforced masonry section- 2-12 and 2-13).
Bullet point 3 points back to unreinforeced masonry however it only references Fa which would be equations 2-12 and 2-13 not eqn 2-11. Where eqn 2-11 is the allowable axial Force (for unreinforced masonry) and what appeared to be the safe guard against critical second order effects. Therefore it does not seem that there is a check or limit to prevent premature failure due to ‘second order’ effects. Or is it the codes intent that eqn 2-11 should apply as well? Any clarification or further insight you can offer would be greatly appreciated.
EIT
Here is what I find in the code:
I will use eqn numbers from 318-05 but the concept appears to be the same up through the 2013 code.
I see that for unreinforced masonry there are the following capacity equations:
1. (2) equations for allowable axial stress (one if h/r<99 (2-12) and one if h/r >99 (2-13)).
2. Then the P<1/4*Pe check. (eqn 2-11)
The commentary states that at larger h/r values where moment magnification is more critical the allowable axial load is limited by equation 2-11. The commentary then explains that Pe is a check to safeguard against premature buckling with loads applied at large eccentricities. It also states that ‘e’ is the actual eccentricity not the ‘virtual eccentricity’ caused by M/P where M is due to other loadings i.e. lateral loads. Therefore it seems that eqn 2-11 eliminates stability concerns in slender sections related to secondary moments for unreinforced sections.
For reinforced masonry there are the following criteria:
1. (2) equations for axial capacity. (2-17 and 2-18)
2. Combined compressive stress must be less than f’m/3
3. Axial component (only) must be less that Fa (which are the 2 equations found in the unreinforced masonry section- 2-12 and 2-13).
Bullet point 3 points back to unreinforeced masonry however it only references Fa which would be equations 2-12 and 2-13 not eqn 2-11. Where eqn 2-11 is the allowable axial Force (for unreinforced masonry) and what appeared to be the safe guard against critical second order effects. Therefore it does not seem that there is a check or limit to prevent premature failure due to ‘second order’ effects. Or is it the codes intent that eqn 2-11 should apply as well? Any clarification or further insight you can offer would be greatly appreciated.
EIT
