Curved Beam

Design of a Curved Beam Concrete grade:

M

IS4995 15

Steel grade:

Fe

415

Beam Geometry: Width, b = Overall depth, D = Reinforcement diameter = Clear cover = Effective depth, d =

500 mm 700 mm 12 mm 44 mm 650 mm

Support width =

350 mm

Load Analysis: Uniformly distributed dead load, ω ∆ =

75 kN/m kN/m

Uniformly distributed live load, ω L = Total uniformly distributed factored load, ω = Radius of the circular beam, r = Half the angle that the arc subtends at the origin of the beam, α = = SF at a support V O = Total load on curved beam = Distance of load from the origin = Sagging moment at midspan: Moment of the external load about the chord, M = Maximum sagging moment , MO =

25 kN/m kN/m 150 kN/m kN/m 4.5 m 22.5 degree degree 0.39 rad 265.07 265.07 kN 530.14 kN 4.39 m

120.75 kN kN-m 78.88 78.88 kN-m kN-m

Maxm SF at support:

β= 180 deg = Shear force at any point at an angle β = Total load on curved beam acts at a distance from origin =

3.14 rad -1855.5 -1855.5 kN 2.86 m

Hogging moment at support centre: β=  At support centre: Maximum hogging moment at centre of support =

0 rad -157.77 kN kN-m

0 deg =

Torsional moment at a section: Orientation of a section having maximum torsional moment at an angle β: Sin β O = 0.17 β O = 0.17 rad 9.53 deg Maximum torsional moment, T β = 11.99 11.99 kN-m kN-m Design: Number of supports = Center-to-center span = Dist of sect of ma maxm torsnl momnt from the ce centr line of of suprt = Clear span =

8 nos 3.53 m 0.75 m 3.18 m

Maximum shear force at the face of the support = Shear force at the section of maximum torsional moment = Equivalent shear, V e =

238.82 kN 152.78 kN

191.13 kN Design at FACE

CHECK for shear design criteria =

β face =

0.04 rad

Torsional moment at the face of the support = Equivalent shear, V e =

5.26 kN-m 255.66 kN

Equivalent nominal shear stress, τ e =

0.79 N/sq mm

Maximum permissible shear stress, τ c max =

2.5 N/sq mm

CHECK for maximum permissible shear stress = Assuming p t =

OK

Permissible shear stress, τ c =

0.35 N/sq mm REQUIRED

0.25 %

CHECK for necessicity of torsion reinforcement = Longitudinal reinforcement  Moment at the face of the support: Equivalent bending moment, M t =

-113.57 kN-m -7.43 kN-m -121 kN-m 157.77 kN-m

Total equivalent hogging BM at the face of the support = Design moment = Coefficients: a= 19.98 b = -234682.5 c = ### A st reqd = 715.9 sq mm x/d = 0.15 CHECK for under or over reinforced section = UNDER REINFORCED Minimum tensile steel required = 665.66 sq mm No of bars at the support top = 7 nos CHECK for bar area provided = OK p t provided = 0.24 % CHECK for reinforcement percentage provided =

REVISE

Transverse reinforcement 

8 Tor stirrups, A

Try 2 legged Clear cover provided all round = b1=

sv

=

100.53 sq mm 25 mm 438 mm

d1= Spacing of stirrups required, x

619 mm reqd

=

208.92 mm

Maximum spacing of stirrups, x max =

166.25 mm

x1=

458 mm

y1=

639 mm 166.25 mm 160 c/c 77.11 sq mm

Optimum spacing required of stirrups = Provide 2 legged Minimum area of stirrups required = CHECK for required area of stirrups

8 Tor stirrups @

Provision of side reinforcement  CHECK for side reinforcement requirement =

OK

NOT REQUIRED

A side steel = Number of

12 Tor bars required =

350 sq mm 4 nos