Advanced Methods of Structural Analysis

Problems 267

RA

H

MA

RB

H

MB

l=2R

O

q

R

Fig. P7.22

Ans.RADqR ; HD0:56012qR; MAD0:10658qR^2

7.23.Design diagram of a two-hinged parabolic arch with the tie is presented in
Fig.P7.23. The equation of the neutral line of the arch is



4f = l^2


x.lx/.The
cross-sectional moments of inertia vary by lawIxDICcos'x.m^4 /. The flexural
stiffness in the highest section of the arch isEIC. The cross-sectional area of the tie
isAt.m^2 /. Modulus of elasticity of the material of the arch and the tie areE.kN=m^2 /
andEt, respectively. Calculate internal axial force in the tie.

y x

P=6m

xq= 12

x

q=2kN/m

f=6m

P=8kN

l=24m

EtAt

EIC

Fig. P7.23

Ans.X 1 D

8558:67

517:082C24ˇ

;ˇD

EIC

EtAt

.

7.24.A rigid horizontal weightless beam is supported by three identical vertical
rods at points 1-3. The beam supports a loadP, as shown in Fig.P7.24. The stiffness
EAis constant for all vertical rods. Determine the axial forces in members 1-3.

P

d d l

1 2 3

Fig. P7.24

Ans.N 1 D0:833PI N 2 D0:333PI N 3 D0:167P.