Advanced Methods of Structural Analysis

582 Appendix

Ta b l e A. 2 3 Reactions of compressed-bent beams;Dl

r

P

EI

Beam under concentrated loadF

and axial compressive forceP

Beam under uniformly distributed

loadqand axial compressive forceP

Pinned–pinned
beam

P P

F

l/ 2 l/ 2

P

l

P

q

M



l

2



D

Fl

2

tan



2

y



l

2



D

Fl^3

2 EI^3



tan



2





2



M



l

2



D

ql^2

^2



sec



2

 1



y



l

2



D

ql^4

EI^4



sec



2

 1 

^2

8



Pinned-clamped
beam

F

P

l/ 2 l/ 2

P P

l

P

q

M.l/DFl

sin



2



1 cos

2



sincos

M



l

2



DFl

sin



2

sincos



0

B@cos

2



sin



2





1

2

1

CA

M.l/D

ql^2

2

2 sin 2 cos

sincos

Clamped-clamped
beam

P P

F

l/ 2 l/ 2

P

l

P

q

M



l

2



D

Fl

2

tan



4

M.0/DM.l/D

Fl

2tan



4

y



l

2



DFl

3

EI^3



tan



4 



4



M



l

2



D

ql^2

2^2



csc



2

 2



M.0/DM.l/D

ql^2

^2



1 



2

cot



2



y



l

2



D

ql^4

2 EI^3



tan



4





4