Calculation of a Rib of a TT-shaped Floor Slab 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 and a concrete strip between the 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. 56-57.

Initial data file:

when the lateral force is Q = 62 kN — Example 12.1.SAV
report – Arbat 12.1.doc.
when the lateral force is Q = 58,4 kN — Example 12.2.SAV
report – Arbat 12.2.doc.

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

Initial data:

b×h = 85×350 mm	Slab rib section sizes
а = 35 mm	Distance from the center of gravity of the longitudinal       reinforcement to the fiber of the section under the greatest tension
d = 8 mm	Diameter of transverse reinforcement
sw = 100 mm	Spacing of transverse reinforcement
q = 21,9 kN/m	Load on the rib
qv = 18 kN/m	Temporary equivalent load
Qmax = 62 kN	Lateral force on the support
Concrete class В15 Class of reinforcement А400

 

ARBAT initial data when the lateral force is Q = 62 kN:

 

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 = 85 mm h = 350 mm a1 = 32 mm a2 = 32 mm	S1 - 2Ø6 Transverse reinforcement along the Z axis 1Ø8, spacing of transverse reinforcement 100 mm

 

Reinforcement	Class	Service factor
Longitudinal	A400	1
Transverse	A400	1

Concrete:

Concrete type: Heavy-weight
Concrete class: B15

Service factor for concrete
γb1	allowance for the sustained loads	1
γb2	allowance for the failure behavior	1
γb3	allowance for the vertical position during concreting	1
γb4	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 kN*m
Q_z = 62 kN
M_z = 0 kN*m
Q_y = 0 kN
T = 0 kN*m
Factor for sustained load 1

ARBAT initial data when the lateral force is Q = 58,4 kN:

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 = 85 mm h = 350 mm a1 = 32 mm a2 = 32 mm	S1 - 2Ø6 Transverse reinforcement along the Z axis 1Ø8, spacing of transverse reinforcement 100 mm

 

Reinforcement	Class	Service factor
Longitudinal	A400	1
Transverse	A400	1

 

Concrete:

Concrete type: Heavy-weight
Concrete class: B15

Service factor for concrete
γb1	allowance for the sustained loads	1
γb2	allowance for the failure behavior	1
γb3	allowance for the vertical position during concreting	1
γb4	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 kN*m
Q_z = 58,4 kN
M_z = 0 kN*m
Q_y = 0 kN
T = 0 kN*m
Factor for sustained load 1

Comparison of solutions:

Check	strength in a concrete strip between oblique sections	strength for an oblique section
Guide	62/68,276 = 0,908	58,4/63,97 = 0,913
ARBAT	0,908	0,912
Deviation, %	–	0,11

Comments:

1. 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.
2. The member length has to be specified in ARBAT. Since it is not defined in the problem, it is taken as 1 m.
3. 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 = а – d/2 = 35 – 6/2 = 32 mm.