Beam Deflection Analysis
Objective: Calculate beam deflection
Task: Calculate the value of beam deflection
References: Practical calculation of elements of reinforced concrete structures according to DBN V. 2.698:2009 in comparison with calculations according to SNiP 2.03.0184* and EN 199211 (Eurocode 2) / V.M. Babaev, A.M. Bambura, O.M. Pustovoitova et.al., edited by V.S. Shmukler, – Kharkiv: Golden Pages, 2015. – p. 280. (Example 15, p. 92.)
Initial data file:
ARBAT mode – SingleSpan Beam Deflection
Example15.1DBN.sav
report – Arbat15.1DBN.doc
Compliance with the codes: DBN V 2.698:2009, DSTU B.V 2.6156:2010
Initial data:
l=6,0 m 
Beam span 
b×h = 200×500 mm 
Beam section sizes 
а = 26 mm 
Distance from the edge of the reinforcement to the edge of the section 
A_{s} = 1232 mm^{2} (2Ø28) 
Crosssectional area of reinforcement 
q= 35,555 kN/m 
Uniformly distributed load 
Concrete class 
С20/25 
Initial data in ARBAT:
Importance factor γ_{n} = 1
Member length 6 m
Section
b = 200 mm h = 500 mm a_{1} = 26 mm a_{2} = 26 mm



Reinforcement 
Class 
Additional service factor 

Longitudinal 
A400C 
1 
Transverse 
A240C 
1 
Specified reinforcement
Span 
Segment 
Length (m) 
Reinforcement 
Section 

span 1 
1 
6 
S1  2Ø28 Transverse reinforcement along axis Z 2Ø16, spacing of transverce reinforcement 100 mm

Concrete
Concrete type: Heavyweight
Concrete class: C20/25
Aggregate: Quartzite
Additional parameters 


Additional service factor 
1 


Age of concrete (days) 
28 


Cement strength class 
Class R 


Creep development time 
36500 
days 

Temperature T(Dt) 
20 
°C 

Number of days when the temperature T prevails Dt 
28 
days 

Relative humidity 
40 
% 

Calculated deflections
Span 
Maximum deflection 
Minimum deflection 


Value 
Snap 
Value 
Snap 


mm 
m 
mm 
m 


span 1 
19,107 
3,012 
0 
6 

Comparison of solutions
Check 
Deflection value 
Guide 
22,2 mm 
ARBAT 
19,107 mm 
Deviation, % 
16,2 % 
Comment. The difference in the results is due to the fact that the Manual uses approximate empirical formulas for determining deflection, based on the use of curvature in the section with the maximum bending moment. In the ARBAT program, deflection is determined at the corresponding curvatures in different sections along the length of the beam.