# TSC Axial strength or Combined Flexural and Axial Strength

Nominal flexural and axial strength is calculated automatically.

Nominal axial compressive strength is calculated automatically.

Nominal axial tensile strength is calculated automatically.

**Notation**

**A _{c }**

**gross area of concrete section,**

_{ }=

**A**_{s}**area of nonprestressed longitudinal tension reinforcement,**

_{ }=

**A**_{st }**=**total area of nonprestressed longitudinal reinforcement,

*depth of equivalent rectangular stress block,*

**α =***width of compression face of member,*

**b**_{w }=*distance from extreme compression fiber to neutral axis,*

**c =**

**C**_{c}**concrete**

_{ }=**compressive force,**

**C**_{s}**reinforcement tension force,**

_{ }=*specified compressive strength of concrete,*

**f**_{ck }=*design compressive strength of concrete,*

**f**_{cd }=*specified yield strength for nonprestressed reinforcement,*

**f**_{yk }=*design yield strength for nonprestressed reinforcement,*

**f**_{yd }=*desing flexural strength at section,*

**M**_{d }=*nominal flexural strength at section,*

**M**_{n }=

**N**_{n}**nominal axial compressive strength of member,**

_{ }=

**N**_{d}**design axial compressive strength of member,**

_{ }=

**N**_{d,max }**=**maximum nominal axial compressive strength of a member,

**N**_{dt}**design axial tensile strength of member,**

_{ }=*net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature*

**ε**_{t }=**k**factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis

_{1 }=**Maximum axial compressive strength**

Nominal axial compressive strength * N_{n}* is limited to a value of

*.*

**N**_{d,max}For nonprestressed concrete members, * N_{d}* shall be calculated by:

According to **TS 500 7.4.1** Maximum design axial compressive strength for a nonprestressed concrete member with closed tie;

The maximum design compressive strength for a nonprestressed concrete member with closed tie;

The design strength of concrete and reinforcement materials is given below.

**Axial tensile strength**

Design axial tensile strength * N_{d,t}* is given

**TS 500 7.4.2**

**Flexural Strength**

Nominal flexural strength * M_{n}* and axial strength are calculated based on the following

*Design Assumptions*.

**Design assumptions**

The flexural and axial strength of a member calculated by the strength design method, two basic conditions should be satisfied:

equilibrium

compatibility of strains

Equilibrium means balancing of forces acting on the element cross section at nominal strength. Stress-strain relationship for the concrete and the reinforcement at nominal strength is established within the design assumptions described follow:

Equilibrium is satisfied at each section.

It is assumed that strain in concrete and reinforcement is proportional to the distance from neutral axis.

Design strength is calculated by using these assumptions together with design assumptions for concrete described follow:

Maximum strain at the extreme concrete compression fiber is assumed equal to 0.003.

Tensile strength of concrete is neglected.

The relationship between concrete compressive stress and strain is represented by equivalent rectangular concrete stress distribution method.

Concrete stress of

is assumed uniformly distributed over. Equivalent rectangular concrete stress zone bounded by edges of the cross section and a line parallel to the neutral axis located a distance**0.85f**_{cd}from the fiber of maximum compressive strain, as calculated by:**α**

The distance between the fiber of maximum compressive stress and the neutral axis,

, is perpendicular to the neutral axis.**c**The value of

is determined using**k**_{1}**TS500 Table 7.1**.

| C16 | C18 | C20 | C25 | C30 | C35 | C40 | C45 | C50 |
---|---|---|---|---|---|---|---|---|---|

| 0.85 | 0.85 | 0.85 | 0.85 | 0.82 | 0.79 | 0.76 | 0.73 | 0.70 |

* N_{d}* means design axial compressive strength and

*means design flexural strength.*

**M**_{d}*takes different values for each axial force level. Therefore, a three-dimensional interaction failure surface shown in the picture above is formed. Nominal flexural strength*

**M**_{d}*is calculated according to the assumptions described in title.*

**M**_{n}Design flexural strength * M_{d}* with zero compression is calculated as described in the title of TSC Flexural Strength . Similarly, with the same design assumption combined design flexural and axial strength

*and*

**M**_{d}*are calculated as shown below.*

**N**_{d}From the equation of equilibrium:

Desing flexural strength * M_{d}* combined with

*is calculated as shown below.*

**N**_{d}

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