huangyhg

calc. reactions for propped cantilever
hi! need some help here.
i've got a propped cantilever on which acts a udl.
i'm trying to find the ractions at the supports and the built in moment if there is any. reaction is at some distance from the free end.
anyone can show me how to proceed?
thx
when you say a propped cantilever, i am picturing a single span beam that is fixed at one end and pinned at the other. the steel manual has this as case 12 in the 13th edition manual (pg 3-214).
the reaction at the pin support is 0.375wl, the reaction at the fixed support is 0.625wl.
assume the support is fixed. and the cantilever subjects to uniform distributed load (udl) "w".
the reactions at a distance "x" from the free end are simply:
shear (v) = w*x
moment (-m) = -w*x*(x/2) = -w*(x^2)/2
(-) means tension on the loading side of the cantilever.
without external loads, the cantilever will have reactions due to self-weight alone.
hope i understood your question, and have answered correctly.
if, by propped cantilever, you mean a condition with two pin supports and one end cant'ing out, this is a simple statics problem.
hello all!
here's a drawing to illustrate what i'm talking about.
i want to calculate the reactions r and s and also the built-in moment m.
without getting into castigliano's method (my favorite) or some other indeterminate analysis, this is what i would do (if i had to do it by hand).
1. remove the support at s, and calc the deflection of the beam at that location. see 13th edition manual case 19.
also calc the moment at the support under this condition.
2. use case 21 in the 13th ed manual and apply a point load p at the location of the reaction s (using only that point load and not the udl). determine what that force (reaction) needs to be to make the upward deflection equal to the downward deflection of the udl.
3. calc the moment of the reaction s (and not the udl) at the fixed support.
4. your reaction s is already calc'ed (see step 2). the vertical reaction at r is done by summing forces in the y direction. the "built-in moment" (i've never heard that terminology used before), is the algebraic sum of the udl only moment and the reaction,s, only moment.
hope that helps.
a proped cantilever (as you've drawn it) is a singly redundant beam. look up "unit load method". or look up "roark", this is a standard problem.
looking at the other respondants, kslee1000 is given you pointers for a determinate beam which won't work out. structuraleit's first post may be right for the shear reactions but lacks the moment (which you could calculate, if the shear's are right, but i suspect they are for a cantilever propped at the end).
if i were to do it by hand, i'd use moment distribution.
a picture/sketch better than thousand words!
lets lable the fixed end as "b", the simple support as "a", the distance from free end to the simple support as "a", the distance in between supports as "b", the total beam length as "l = a+b". now solving the reaction at the simple support by consistent displacement method:
1. displacement at "a" for a cantilever with legth "l" and udl "w" equals:
w*(a^4-4al^3+3l^4)/(24ei)
2. displacement at "a" for the same cantilever with a concetrate load "p" equals:
p*b^3/(3ei)
3. equate displacements from 1 & 2 you can solve force p, which is the reaction of support a. from there on, you can solve the reactions at the fixed support by simple statics.
above equations can be found at many structural analysis text books, as well as the aisc beam manual. please verify.

run it through risa or other software
structuraleit and kslee1000 have got it.

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