structural

Question 1

flexibility method steps

Answer 1

support reactions
draw shear and moment diagrams
evaluate determinacy (no of unknowns - no of equations)
degree of determinacy = no of redundant reactions
n of unknowns > n of equations -> indeterminate

Question 2

flexibility method: stat determinate structures

Answer 2

choose redundant
redraw structure with removed redundant
no of drawings = degree of determinacy +1
primary structure -> external load applied to structure
secondary structure -> redundant reaction reintroduced as external LOAD not a reaction

Question 3

flexibility method: compatibility

Answer 3

actual displacement = primary displacement + redundant displacement
choose analysis method to solve for displacements (likely virtual force/work)

Question 4

virtual work

Answer 4

external virtual work = internal virtual work
steps:
draw internal shear/moment diagram for real loading
apply unit virtual load where we want deformation
find internal loads
draw V/M diagram for virtual
1*displacement=integral of-> 1/EI virtual momentreal moment dx
(using product integral for integral part)

Question 5

moment distribution: pinned end

Answer 5

flexural stiffness coefficient k= 3ei/L

carry over moment= 0

Question 6

moment distribution: fixed end

Answer 6

flexural stiffness coefficient k= 4ei/L

carry over moment Mba=Mab/2

Question 7

moment distribution: distribution factors

Answer 7

for a beam with supports at A->B->C
Dba = kba / (kba +kbc)
Dbc = kbc / (kba + kbc)

Question 8

moment distribution steps

Answer 8

k factors (4ei/L or 3ei/L)
dist. factors
find end member moments using table (initial moments)
find nodal moments if any
1. sum moments if needed
2. find moments of each side by multiplying moment by dist factors and balance
3. carry-over moments (half for fixed, zero for pinned)
4. go to step 1.

do steps until carry over gets low enough, then stop and add columns up
use moments from each column to draw moment diagram

if there is a load on a beam where the end member is pinned (dist = 0) the moment created has to be balanced with an opposite/equal moment and carried over to the other end of the beam.

Question 9

slope deflection method

Answer 9

M i j = 2ei(2theta i+theta i+3psi i j) + FEM
where psi is support settlement or displacement and = delta/L
degree of stat int. = (# of unknown reactions + internal forces) - (# equi eqs. at each node)
DOKI = # of independent nodal displacements that are free to take place (translations and rotation)

Question 10

slope deflection method: pin jointed frames

Answer 10

DOSI = members + reactions - 2nodes
above zero = stat determinant
DOKI = 2n-r

Question 11

slope deflection method: rigid jointed frames

Answer 11

DOSI = 3m+r-3n
DOKI = 3n-r

Question 12

slope deflection method: continuous beams

Answer 12

DOSI = 3m+r-3n
DOKI = 3n-r