ULS strength analysis

For a strength analysis there are several criteria that may govern the strength of the section. For a concrete (compression) governed section:

• axial force = applied axial force

• moment angle = applied moment angle

• concrete strain: concrete failure strain = 1

For a reinforcement (tension) governed section:

• axial force = applied axial force

• moment angle = applied moment angle

• rebar strain: rebar failure strain = 1

Some codes implement a third condition which limits the compressive strain on the section when the whole section is in compression.

Strength reduction or material partial factors for ULS

There are two main approaches applicable to section analysis: strength reduction and material partial factors. The strength reduction approach is use in the ACI (American) and AS (Australian) codes. In this case the material strengths are used unfactored, the strength of the section is calculated and then reduced using a strength reduction factor $\varphi$. The particular value of $\varphi$ depends on the strain place at failure.

For example, as per ACI 318M-14 Fig. 21.2.2-b,

In most other codes factors are applied to the material in the ULS. Giving a reduced strength for the material in design

$$f_d=\frac{f}{\gamma_m}$$

The CSA (Canadian) codes use a similar approach but use a factor $\varphi_m$.

$$f_d=\varphi_mf$$

The values of $\gamma_m$ and $\varphi_m$ are specified in the code but typical values are

	$\gamma_m$	$\varphi_m$
Concrete	1.5	0.65
Reinforcement	1.15	0.85
Pre-stress tendons	1.15	0.9
Structural steel		0.9