Topic: EXTERNAL SUPPORT REACTIONS Notebook

The first step in most structural analysis is

to compute the support reactions for a

given

structure m

That is the external forces required tomaintain

equilibrium

E Fi O EEy 0 EM 0

o Note that internal hinges can add a challenge

to determining reactions

To handle them we'll t.im do thefollowing 時

hinge
o Recognize that at the hinge the sum

of moments must be zero

Example Ii

Compute the support reactions of the beam shown

20K 115K 16K

t 心 に 8

Ag参 参
40 T

yAy By

o
会t

o
Ay By 0

EM 0 20410 15.20 10.32 By 40

By 25.3 K
25.3K

Ay

Example 2

Compute the support reactions for the cantilever

beam shown at 10K 20k

An

M N 10
x x

会 10K
10K
f GR
201 28 K

Ay
M 20 K G20 104た 10 400 80 480fk

Topic: EXTERNAL SUPPORT REACTIONS Notebook

Example 3

20k 30k Compute the supportreactions

t.li さ on theframe shown

心 まち

で 詔 RB

Af炎A

x ix wi
x

Ay
を 0 2じ 10 20110 30.20 な R 20 3，30

Ma 10005K
こ

RB 16 18

RB 1000134 29.41
k

Aai GRB 20に 3.53

Ay 20 30
EB 32.35

Example 4
ニ G 18kip

B C v D

Determine reaction

だ 1
for theframe

i is 12 below

が iI CC hinges

A Aa Ee E

為 12
i
12 参

k た t

tAy

a
TEy.IM
で 0 17 G t 18 18
31.5 K
Ey 24

Ey

K K
えな O の 31.5 18 B5
Ay

o こ

K.EE

0 Aat E 72

Cos a hinge

EM に 0 E 124 184 G Ey 12公

で
Ewe

Topic: EXTERNAL SUPPORT REACTIONS Notebook

Example 5

Compute the reactions for the beam below

Notice the internal hinge and bad at Ti

AI で2Kip paKip
I

た E

参
x o B
x
ら x
がD
x

背器で品々as

な参
lo B
x
ら
火が D I
た E EMA 20
12.15 24.20 Ey25
x x x

た TBy TEy こ
By10

の
Byた 36 hi
I Fye Oe Aye Rt24 By Ey

12Kop

Example 6 4 50k

t.skft いく が

30
週
It Ill が

At X At At

XWtt X X

Example7

compute the reactions the beam belowfor

Notice the internal hinges at と and KD

t100kip 2KipIft
u t t
1
t t t t 0t t t t 0t t t t t t t t t tu

金A B が D E F

90
fy120
o go X NO

x x x x x

tNO呦 2KipIft

Ait1 t t t t t t 0t t t t 0t t t t t t t t t tu

金A B が D TE n F
fy

AyTx o T x
By 90
x
120
x go XEy wt x Fy

twoKip
L L t t t Ntt

Segment CD が
2.1201607120 Dy 1100

gt TryRi

Dyこ 145K 100 2.120

Topic: Notebook

Segment ABC

に
2145 195K

hit it t.tt

参A 参B I 三た
1 0

C K

TAy TBy の By 100た 21100 195 ら

100 x が 望

e By 731.5K

o
Ay 195 2.400 90 By

a 156.5 K t

Segment DEF

2KHt 三M 0

1454 t t l l t.ir p た

で I e Ey NO K5 190 2型

D E 品 F

Go Ef 100 IFy e Eye 636.5 K

Fyi To

145 2.190 636.5

111.5 K t

Ertyggggggh

abc

Topic: Notebook