Advanced Methods of Structural Analysis

Problems 367

a 13452689107 11

ll

268104

ll

b

Fig. P10.7

Ans. (a) Ordinate of IL.Z/at point 8 is0:0274



l^2 =EI



I M 1 D5:48l;

M 6 D10:96l.

10.8.Pinned–pinned–pinned beam is subjected to concentrated loadPIulD0:4l
(Fig.P10.8).
(a) Construct the the influence line for angle of rotation at the middle support; (b)
Calculate the bending moment at the support 1; (c) Calculate the vertical displace-
ment at sectionkand show the elastic curve.

2

P

l l

0.5l

k

01

ul ul

Fig. P10.8

Ans.M 1 D0:096P l; fkD0:006



Pl^3 =EI



10.9.Design diagram of the frame is shown in Fig.P10.9. Bending stiffness for all
members isEI.
(a) Construct the influence lines for bending moment and shear at sectionk.
(b) Construct the bending moment diagram if the fixed loadPD 10 kN is located
on distance0:6lfrom the left support, i.e. in the section 3; (c) construct the bending
moment diagram if the fixed loadP D 100 kN is located on distance0:6lfrom
the rigid joint, i.e. in the section 8.Hint: Divide each span by five portions. Joints
numeration is shown in Fig.10.4. For problems (b) and (c) use the influence line for
primary unknown.

Ans.
(a)M 1 D0:09312lI MkD0:19296l : : : ; Q 1 D0:2672IQkleftD0:5176 : : :I

(b)M 3 D1:5936l .kN m/IM 5 leftD1:344lIM 5 rightD0:768lIM 10 D0:384l;

(c)M 5 leftD2:88lIM 5 rightD5:76lIM 8 D11:904lIM 10 D16:32l