CIVIL ENGINEERING FORMULAS

118 CHAPTER FIVE

Negative moment at face of all supports for

(a) slabs with spans not exceeding 10 ft (3 m)

and (b) beams and girders where the ratio of

sum of column stiffness to beam stiffness

exceeds 8 at each end of the span

Negative moment at interior faces of exterior

supports, for members built integrally with

their supports

Where the support is a spandrel beam or girder

Where the support is a column

Shear Forces

Shear in end members at first interior support

Shear at all other supports

End Reactions

Reactions to a supporting beam, column, or wall are obtained as the sum of shear
forces acting on both sides of the support.

DESIGN METHODS FOR BEAMS,
COLUMNS, AND OTHER MEMBERS

A number of different design methods have been used for reinforced concrete con-
struction. The three most common are working-stress design, ultimate-strength
design, and strength design method. Each method has its backers and supporters.
For actual designs the latest edition of the ACI Codeshould be consulted.

Beams

Concrete beams may be considered to be of three principal types: (1) rectangu-
lar beams with tensile reinforcing only, (2) T-beams with tensile reinforcing
only, and (3) beams with tensile and compressive reinforcing.

Rectangular Beams with Tensile Reinforcing Only This type of beam includes
slabs, for which the beam width bequals 12 in (305 mm) when the moment and
shear are expressed per foot (m) of width. The stresses in the concrete and steel
are, using working-stress design formulas,

fc (5.6)

2 M

kjbd^2

fs

M

Asjd



M

pjbd^2

wln 2

1.15wln 2

wl^2 n 16

wl^2 n 24

wl^2 n 12