CIVIL ENGINEERING FORMULAS

CASE 2. Beam Supported Both Ends—Concentrated Load at Any Point

R =

Wb

L

Wa

L

R 1 =

V (max) = R when a < b and R 1 when a > b

At point of load:

Atx: when x = a(a + 2b)+ 3 and a > b

D (max) = Wa b (a + 2b) 3a(a + 2b)+ 27 EIL

Atx: when x < a

Atx: when x > a

Atx: when x < a

LW

D

R R

1

x M

V

ab

Atx: Wb

L

V =

Wa b

L

M (max) =

Wbx

L

M =

Wbx

6 EIL

D =2L (L – x) – b^2 – (L – x)^2

Wa (L – x)

6 EIL

D =2Lb – b^2 – (L – x)^2

FIGURE 2.2 Beam formulas. (From J. Callender, Time-Saver Standards for Architectural Design Data, 6th ed., McGraw-Hill, N.Y.)

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