ABSTRACT
TERMS AND SYMBOLS: a is a measured distance along the beam, in or ft b is another measured distance along the beam, in or ft E is the modulus of elasticity, psi or ksi I is the moment of inertia of the beam, in4 l is the length of the beam between reaction points, in or ft M is the maximum moment, inlb, ftlbs, kip ft, or kip in max M I is the maximum moment in the left section of the beam M2 is the maximum moment in the right section of the beam Mx is the moment at distance x from the left end of the beam P is a point load, lbs or kips P I is the point load nearest the left reaction P 2 is the point load nearest the right reaction and is not equal to PI
R is the end beam reaction of any condition of symmetrical loading, lbs or kips R I is the left end beam reaction R2 is the right end beam reaction V max is the maximum vertical shear for any symmetrical loading condition, lbs or kips VJ is the maximum vertical shear in the left section of the beam, kips V2 is the maximum vertical shear at the right reaction point, or to the left of the inter-
mediate reaction point of the beam V3 is the vertical shear at the right reaction point, or to the right of the intermediate
reaction point of the beam Vx is the vertical shear at distance x from the left end of the beam W is a total uniformly distributed load on a beam, lbs or kips w is a uniformly distributed load per unit of length, pli, plf, kips/in, or kips/ft x is any distance measured along the beam from the left reaction, in or ft x I is any distance measured along the overhang section from the nearest reaction point,
in or ft .1max is the maximum deflection, in .1a is the deflection at the point of load, in t.x is the deflection at any point x distance from the left reaction, in .1xJ is the deflection of the overhanging section at any point x J measured from R2, in
BEAM DIAGRAMS AND FORMULAS, continued for various static loading conditions
2. SIMPLE BEAM, concentrated load at center I-r---(---~I ~x-1 ( i i R=-V max M (at center)
max
~ (at center) max
P 2 PI
48EI Px 2
=- ~(3I2 _4X2) 48EI
BEAM DIAGRAMS AND FORMULAS, continued for various static loading conditions
max I
= Px
BEAM DIAGRAMS AND FORMULAS, continued for various static loading conditions
M (at fixed end) R max
~ (at free end) max
M x
~ x
max M (at fixed end)
max
~ (at free end) max
M x
~ x
a
= wi
2 wl 4
wx 2 =
= -- x -41 x+31 w (4 3 4) 24El
:::p
= PI PI) 3EI
= ~(2/3 _3/ 2 X+X3) 6El
BEAM DIAGRAMS AND FORMULAS, continued for various static loading conditions
6EIl
