A complete process to design a gantry crane form wheels to girder.
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DESIGN OF R.C.C. GANTRY BEAM
1. Desi Design gn data data : Gantry beam is designed as simply supported beam resting on corbels. :
Load carrying capacity of crane Span of gantry beam ' l ' Wheel base of crane Weight (approximately) (approximately) Weight on a wheel / wheel load Weight of crab Grade of concrete Reinforcement Size of gantry beam Width Depth Clear cover to reinforcement Self weight of Beam + rail load Wheel load considering impact of 18.00 + 18.00 x 25 /100 = 22.50 Ton
: : : : : : : : : : : : :
25.00 6.00 4.00 19.00 18.00 13.00 M 25 Fe 415 400 600 30 8.00 25 225
Ton m m Ton Ton Ton
mm mm mm kN/m % kN
2. Analysis of the beam beam : For maximum Bending Moment : Case I : one of the load and the C.G. of the moving load are equidistance from the centre of beam span. C.G. of loads 225.0 kN
8.0 kN/m A
C
1.00
225.0 kN D
1.00
B
4.00 3.00
3.00
RA = 174.0 kN
RB = 324.0 kN
centre of beam
Support reaction RA = {(225.0 x 4.00) + (225.0 x 0.00) + (8.0 x 6.00 x 6.00 /2)}/6.00 = 174.00 kN RB = {(225.0 x 6.00) + (225.0 x 2.00) + (8.0 x 6.00 x 6.00 /2)}/6.00 = 324.00 kN MC = {(174.0 {(174.0 x 2.00) 2.00) - (8.0 x 2.00 x 2.00 2.00 /2)} = 332.00 kN m MD = {(324.0 {(324.0 x 0.00) 0.00) - (8.0 x 0.00 x 0.00 0.00 /2)} = 0.00 kN m Case II : one of the wheel load is at centre of the span. 225.0 kN
8.0 kN/m
A
C 3.00
RA = 136.5 kN
C:\gantry & corbel
B 3.00 RB = 136.5 kN
Page No.
Support reaction RA = {(225.0 x 3.00) + (8.0 x 6.00 x 6.00 /2)}/6.00 = 136.50 kN RB = {(225.0 x 3.00) + (8.0 x 6.00 x 6.00 /2)}/6.00 = 136.50 kN MC = {(136.5 x 3.00) - (8.0 x 3.00 x 3.00 /2)} = 373.50 kN m For maximum Shear Force: 225.0 kN
8.0 kN/m
A
225.0 kN
C
B 4.00 6.00
RA
= 174.0 kN
RB
= 324.0 kN
Support reaction RA = {(225.0 x 4.00) + (8.0 x 6.00 x 6.00 /2)}/6.00 = 174.00 kN RB = {(225.0 x 6.00) + (225.0 x 2.00) + (8.0 x 6.00 x 6.00 /2)}/6.00 = 324.00 kN Design / Factored Span Moment Mmax = 373.50 x 1.5 = 560.25 kN m & Factored Shear Force Vmax = 324.00 x 1.5 = 486.00 kN
\
For Transverse Breaking Force : Transverse breaking force per wheel = 10% of (weight to be lifted + weight of crab)
T.B.F. = 10 % (25.0 + 13.0) = 3.80 Ton = 38.0 kN Hence total transverse breaking force on gantry beam = 38.0 x 2 = 76.0 kN Considering the rail height = 150 mm Eccentricity of T.B.F.
: =
Moment due to eccentricity
: =
Factored Torsional moment T u
C:\gantry & corbel
: =
600 / 2 + 150 450.0 mm 2 x 38.0 x 0.45 34.2 kN m 1.5 x 34.20 51.3 kN m
Page No.
Equivalent Bending Moment M e = M u + M t
where, M u = bending moment at the cross-section, 51.3 [{1+(600/ 400)}/1.7] = M e = 560.25 + 75.44 =
\
Equivalent Shear V e = V u + 1.6 T u / b =
75.44
kN m
635.69 kN m
691.20 kN
3. Balance Design Parameters : ku = 700 / (1100 + 0.87 f y) = 0.48 Ru = 0.36 f ck ku (1 - 0.42 ku) 2
= 3.44 N/mm p t = (0.36 f ck / 0.87 f y) x ku x 100 =
1.19
%
4. Design for Flexure : Moment of resistance of the section M cr = Ru b d2 = 428.97 kN m <
M e =
635.69 kN m
Design Beam as Doubly Reinforced Section. Area of tension reinforcement required
mm f bars. Use 25 Nos of bar required = 8 Provide nos of bar = 8 Ast provided = 3927.0 mm2 Area of compression reinforcment required
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esc
= 0.0035 {1 - d' /(ku d)} c = 0.0035 {1- 52.5/(0.48 x 547.5)} = 0.0028
From IS 456 : 2000, cl. 38.1 and fig. 23A 2 f sc = 0.976 f y /1.15 = 352.2 N/mm f cc = 0.446 f ck = \
N/mm2
11.2
Asc = 1186.84 mm2
mm f bars. Use 25 Nos of bar required = 3 Provide nos of bar = 3 Ast provided = 1472.6
2
mm
5. Check for Shear : Equivalent shear force V e = Shear stress
tve
=
691.20 kN
691.20 x 1000 / (400 x 600) = 2.88 N/mm2 < 3.10 N/mm2 (Max. permissible shear stress)
Percentage of steel provided p t =
1.76 %
Design shear strength of concrete with amount of reinforcement provided (Ref. IS 456 : 2000, table19) tc
=
0.78
N/mm2
Transverse Reinforcement required
where, T u = V u = sv = b1 =
torsional moment = 51.3 kN m shear force = 486.00 kN spacing of the stirrup reinforcement = 135 mm c/c distance between corner bars in the direction of the width 315 mm = d 1 = c/c distance between corner bars = 521.5 mm b= breadth of the member = 400 mm
\ A sv =
256.15 mm2
Minimum transverse reinforcement required
where, t ve = equivalent shear strength t c = shear strenght of the concrete \ A svmin = 313.47 mm2 C:\gantry & corbel
