TSC Axial strength or Combined Flexural and Axial Strength

Notation

A_c = gross area of concrete section,
A_s = area of nonprestressed longitudinal tension reinforcement,
A_st = total area of nonprestressed longitudinal reinforcement,
α = depth of equivalent rectangular stress block,
b_w = width of compression face of member,
c = distance from extreme compression fiber to neutral axis,
C_c = concrete compressive force,
C_s = reinforcement tension force,
f_ck = specified compressive strength of concrete,
f_cd = design compressive strength of concrete,
f_yk = specified yield strength for nonprestressed reinforcement,
f_yd = design yield strength for nonprestressed reinforcement,
M_d = desing flexural strength at section,
M_n = nominal flexural strength at section,
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,
ε_t = net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature
k₁ = factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis

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:

1. equilibrium

2. 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 0.85f_cd 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 α from the fiber of maximum compressive strain, as calculated by:

• The distance between the fiber of maximum compressive stress and the neutral axis, c, is perpendicular to the neutral axis.

• The value of k₁ is determined using TS500 Table 7.1.

N_d means design axial compressive strength and M_d 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_n is calculated according to the assumptions described in title.

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 M_d and N_d are calculated as shown below.

Open

From the equation of equilibrium:

Desing flexural strength M_d combined with N_d is calculated as shown below.