Strength of normal section (double bending with compression). Nonlinear deformation model

Objective: Check the strength of the section by nonlinear deformation model

Task: Determine the relative strains in the compressed concrete and in the tensile reinforcement

References: E.N. Kodysh, N.N. Trekin, I.K. Nikitin, K.E. Sosedov. Practical methods and examples of calculation of reinforced concrete structures from heavy concrete according to SP 63.1330. - Monograph. M.: Publishing and printing enterprise of LLC “Bumazhnik”, 2017. - 496 с. (Example 15, pp. 192-198)

 

Initial data file:

ARBAT program section – Check, mode – Strength of RC Sections
Example-15-SP.SAV
отчет – Arbat 15-SP-dm.doc

Compliance with the codes:  СП 63.13330.2012.

 

Initial data:

b×h = 300×600 mm	Cross-section sizes
а = 54 mm	Distance from the edge of the lower reinforcement to the lower edge of the cross-section (protective layer)
As = 4826 mm2 (6Ø32)	Area of the reinforcement
N = 2000 kN	Longitudinal compressive force
Мy = 250 kNm	Bending moment around Y axis
Мz = 100 kNm	Bending moment around Z axis
Concrete class Class of reinforcement	В25 A400

 

Initial data in ARBAT:
Importance factor  γ_n = 1
Importance factor (Serviceability limit state)  1
Member length 1 m
Effective length factor in the XoY plane 1
Effective length factor in the XoZ plane 1
Random eccentricity along Z according to SP 63.13330.2012
Random eccentricity along Y according to SP 63.13330.2012
Structure is statically determinate
Limit slenderness - 200

 

Section

b = 300 mm h = 600 mm a1 = 37,5 mm a2 = 37,5 mm	S1 - 2Ø25 + 1Ø25 S2 - 2Ø25 + 1Ø25 S3 - 1Ø25

 

Reinforcement	Class	Additional service factor
Longitudinal	A400	1
Transverse	A240	1

 

Concrete

Concrete type: Heavy-weight
Concrete class: B25

Additional parameters
γb1	allowance for the sustained loads	1
γb2	allowance for the failure behavior	1
γb3	allowance for the vertical position during concreting	1
γb5	allowance forthe freezing/thawing and negative temperatures	1

 

Humidity of environment air - 40-75%

 

Compressed concrete state diagram

 

Results of analysis by load case combinations

	N	My	Qz	Mz	Qy	T	Safety factor for load	Factor for sustained load	Short-term	Seismicity	Special
	kN	kN*m	kN	kN*m	kN	kN*m
1	-2000	250	0	100	0	0	1	1

 

Checked according to SP	Check	Utilization Factor
	Ultimate moment strength of the section	0,50178
Sec. 8.1.20-8.1.30	Strains in compressed concrete	1,00049
Sec 8.1.20-8.1.30	Strains in the tensile reinforcement	1,00239

 

Comparison of solutions

Check	Strains in compressed concrete
Example	0,003409/0,0035=0,974
ARBAT	1,00049
Deviation, %	2,7 %
Check	Strains in the tensile reinforcement
Example	0,0012/0,025=0,048
ARBAT	0,0507
Deviation, %	5,6 %