Bearing Capacity of Cross Section Loaded by Combination of Bending Moment and Normal Force
A cross-section loaded by a combination of bending moment and normal force requires the determination of a neutral axis, dividing the cross-section into a tensile and compressed part. When searching the position of the neutral axis, the influence of buckling is included, i.e. normal force is increased by dividing it by coefficient of buckling χ. The neutral axis is searched following the procedure known from the dimensioning of concrete cross-sections, reinforced by steel, as a limit equilibrium method. Compression is transmitted by a part of a steel reinforcement and cement mixture filling. Tension is taken by the remaining part of the steel reinforcement, the cement mixture in tension, is not considered.
The bearing capacity in bending is determined by the following formula:
where: | Rsd | - | design strength of steel |
As,t | - | area of the tensile part of the steel micropile cross-section | |
As,c | - | area of the compressed part of the steel micropile cross-section | |
Ac,c | - | area of the compressed part of the cement mixture cross-section | |
ts,t | - | location of the center of tensile steel part | |
ts,c | - | location of the center of compressed steel part | |
tc,c | - | location of the center of compressed cement mixture part | |
Rcd | - | design strength of cement mixture in compression |
Design strengths are equal to standard values in the verification based on the factor of safety.
Design strengths of steel and cement mixture are calculated in the verification based on the theory of limit states as follows:
where: | Rs | - | standard strength of steel, entered in the frame "Material" |
γss | - | reliability coefficient of steel, entered in the "Micropiles" tab | |
Rc | - | standard strength of cement mixture in compression, entered in the frame "Material" | |
γsc | - | reliability coefficient of cement mixture, entered in the "Micropiles" tab |
The stress in the steel part of the cross-section is determined as:
where: | M | - | bending moment acting in section |
Mu | - | bearing capacity in bending | |
Rsd | - | design strength of steel |