Shear strength prediction—softened truss model - Reinforced Concrete Deep Beams - page 157

7 Shear strength prediction—

softened truss model
S.T. MAU and T.T.C. HSU, University of Houston

Notation

a shear span; measured centre-to-

centre from load to support

f 1 steel stress in 1-direction

f 1y yielding stress of longitudinal st-

eel reinforcement a' shear span measured from centre

of loading to edge of support

f t steel stress in the t-direction

A v1 cross-section area of horizontal

web steel

f ty yielding stress of transverse steel

reinforcement;

b thickness of beam f y yield stress of steel reinforcement

stress ratio s r / f ' c

h total depth of beam

C

K ratio of the effective compressive

stress in transverse direction to
the effective shear stress in the
shear element

C 1 limiting constant for reinforcem-

ent index in 1-direction

C s limiting constant for strength

ratio v n / f ' c

l the longitudinal direction; usually

horizontal for a beam;

C t limiting constant for reinforcem-

ent index in t-direction

L clear span of the beam

d effective depth of beam; meas-

ured from extreme compression
fibre to centre of tension reinfor-
cement

p effective transverse compression;

acting on the shear element

R F ratio of calculated shear strength

to test shear strength

d' distance from top surface of the

beam to centre of flexural comp-
ression steel

R T ratio of theoretical shear strength

from softened truss model to exp-
erimental shear strength

d v effective depth of shear element,

taken as d-d' when compression
steel is present and 0.9d when
compression steel is not present

S spacing of vertical reinforcement

S 2 spacing of horizontal web reinfo-

rcement

t the transverse direction; usually

vertical for a beam

E c initial modulus of elasticity of

concrete taken to be -2 f ' c / e o

v effective shear stress in the shear

element

E s modulus of elasticity of reinfor-

cing bars

v n shear strength taken as the maxi-

mum shear stress in the v-vs g lt
curve

f ' c cylinder compression strength of

concrete

f cr cracking strength of concrete, as-

sumed to be

V shear force in the shear span

V n ultimate shear force