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Bearing Capacity of Cross-Section Loaded by Combination of Bending Moment and Normal Force

A cross-section loaded by combination of bending moment and normal force requires the determination of neutral axis, dividing the cross-section into tensile and compressed part. When searching the position of neutral axis, 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 tube and cement mixture filling. Tension is taken by the remaining part of the steel tube, 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