Calculation of a Simply Supported Floor Beam for Load-bearing Capacity under Lateral Forces

Objective: Check of the calculation of the resistance of reinforced concrete sections.

Task: Verify the correctness of the strength analysis of oblique sections.

References: Guide on designing of concrete and reinforced concrete structures made of heavy-weight concrete (no prestressing) (to SP 52-101-2003), 2005, p. 57-58.

Initial data file:
Example 13.SAV
report – Arbat 13.doc.

Compliance with the codes: SP 52-101-2003, SP 63.13330.2012.

Initial data:

b×h = 200×400 мм	Beam section sizes
h₀ = 370 мм	Effective height of the beam section
d = 8 мм	Diameter of transverse reinforcement (two-leg stirrups)
s_w = 150 мм	Spacing of transverse reinforcement
q_v= 36 кН/м	Temporary equivalent load
q_g = 14 кН/м	Permanent load
Q_max = 137,5 кН	Lateral force on the support
Concrete class В25 Class of reinforcement А240

ARBAT initial data:

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 SNiP 52-01-2003 (Russia)
Random eccentricity along Y according to SNiP 52-01-2003 (Russia)
Structure is statically indeterminate
Limit slenderness - 200

Section:

b = 200 mm
h = 400 mm
a₁ = 27 mm
a₂ = 27 mm

S1 - 2Ø6
Transverse reinforcement along the Z axis 2Ø8, spacing of transverse reinforcement 150 mm

Reinforcement	Class	Service factor
Longitudinal	A240	1
Transverse	A240	1

Concrete:

Concrete type: Heavy-weight
Concrete class: B25

Service factor for concrete
γ_b1	allowance for the sustained loads	1
γ_b2	allowance for the failure behavior	1
γ_b3	allowance for the vertical position during concreting	1
γ_b4	allowance for the freezing/thawing and negative temperatures	1

Humidity of environmental air - 40-75%

Crack resistance:

No cracks

Forces:

N = 0 kN
M_y = 0 T*m
Q_z = 100,35 kN
M_z = 0 T*m
Q_y = 0 kN
T = 0 T*m

Factor for sustained load 1

Comparison of solutions:

Check	strength for an oblique section
Guide	100,35/100,69 = 0,997
ARBAT	0,982
Deviation, %	1,5

Comments:

The strength check of oblique sections is performed by comparing a sum of lateral forces resisted by concrete and stirrups in the oblique section (Q_b + Q_sw), with a lateral force Q in the oblique section which is determined as a projection on the normal to the longitudinal axis of the element of the resultant of all external forces acting on the element on one side of the considered oblique section (Q = Q_max– q₁c). In order to check the strength of the oblique section the value of the lateral force in the normal section is taken as Q = 58,4 kN according to the Guide.
The member length has to be specified in ARBAT. Since it is not defined in the problem, it is taken as 1 m.
The data on the longitudinal reinforcement has to be specified in ARBAT. Since it is not defined in the problem, the following reinforcement is used: class А400, rebars 2Ø6. Respectively, the value of the concrete cover is а₁= а₂ = h – h₀ – d/2 = 400 – 370 – 6/2 = 27 mm.