Notations for Concrete Beam Shear Design

b_w

=

Width of beam (web)

d

=

flexural depth of the beam

f’_c

=

concrete compressive strength

f_ct

=

average splitting tensile strength of lightweight concrete

f_y

=

reinforcement yield strength

L

=

beam clear span, from support face to other support face.

N

=

number of stirrups required within a given segment of the beam

N_l

=

number of legs for each stirrup

V_c

=

concrete nominal shear strength

V_s

=

nominal shear strength provide by the shear reinforcement

V_sb

=

nominal shear strength provided by shear reinforcement at the section where Vs is the max permitted by ACI 11.12.1.1 . locating of this section is needed to define which maximum s provisions applies, i.e. §11.5.4.1 or §11.5.4.3

V_{s req’d}

=

required nominal shear strength provided by shear reinforcement.

V_u

=

factored shear force at the face of the beam support

V_{u d}

=

factored shear force at distance d from the face of the support in accordance with §11.3.1.1 this is the critical shear force provided that:

·         support is subjected to compressive force.

·         no concentrated load on the beam within the distance d.

V_{u req’d}

=

factored shear force at the mid-span of the beam, will not be zero if the beam is partially loaded with superimposed loads (i.e. live load on half the beam span)

fV_{n max}

=

reduced shear strength of the beam section located along the beam span where  minimum shear reinforcement is required in accordance with §15.5.5.1

s₁

=

spacing of stirrups within the critical section.

s_k

=

spacing of stirrups within any section subsequent to the critical section.

s_max

=

maximum stirrups spacing permitted by §11.5.4.1 or §11.5.4.3

s_req’d

=

required stirrups spacing at the section considered

x_b

=

the distance along the beam at which V_sb occurs. for any beam section within the distance x_b, V_sb is based on §11.5.4.3, otherwise is based on §11.5.4.1

x_min

=

distance from the face of the support along the beam span after which minimum shear reinforcement in accordance to §11.5.5.1 is no longer required. 

x_max

=

distance from the face of the support along the beam span after which stirrups shall be placed with the maximum spacing per §11.5.4.1, and §11.5.4.3

  s

=

incremental in stirrups spacing between the subsequent sections, suggested to be 1, 2, and or 3 inches