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 verification based on factor of safety.

Design strengths of steel and cement mixture are calculated in verification based on limit states using following formulas:

where:	Rs	-	standard strength of steel, entered in the frame "Material"
	γms	-	reliability coefficient of steel, entered in the frame "Settings"
	Rc	-	standard strength of cement mixture in compression, entered in the frame "Material"
	γmc	-	reliability coefficient of cement mixture, entered in the frame "Settings"

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