# MODEL QUESTION PAPER

B.E. / B. Tech. DEGREE EXAMINATION, APRIL / MAY 2004

Sixth Semester

Civil Engineering

CE336 – STRUCTURAL ANALYSIS II

Time: Three hours                                                                                     Maximum: 100 Marks

### Questions 1 to 10 carry 2 marks each.

Questions 11 to 15 carry 16 marks each.

Make all sketches in pencil only.

1.         In Fig. 1, D is the mid point of AB. If a point load W travels from A to C along the span where and what will be the maximum negative bending moment in AC.

 l/3
 B
 A
 C
 D
 l

2.         In Fig. 1 above, find the position and value of maximum negative shear.

3.         For the beam in Fig. 1, sketch the influence line for reaction at B and mark the ordinates.

4.         Sketch qualitatively the influence line for shear at D for the beam in Fig. 2. (Your sketch shall clearly distinguish between straight lines and curved lines)

 0.8 l
 1.6 l
 C
 D
 B
 l
 A

5.         For the structure in Fig. 3, find the net bending moment at C.

 30 kN

 4m

#### B

 16m

6.         A trestle is pinioned on ball and socket joints at the nodes of an equilateral triangle of side ‘a’ at ground level. The 3 inclined members are ‘a’ m long similarly connected at top. Find the vertical component of compression in each member due to a vertical load of 1.2 kN hanging from the apex.

7.         Fig. 4 shows the plan of a beam ABC. Find the torsion at A due to a downward udl of 0.8kN/m over BC. (Show the torque vector at A)

 A
 6m

 B

 C

8.         AB is a cable over a 48m span. The supports are at different levels as shown in Fig. 5. Find l2.

 48m
 3m
 A
 B
 9m
 l2

9.         Determine the equal area axis of the section shown in Fig. 6. When will this be the neutral axis of the section?

 80

 24
 80
 24

10.        Comment on the behaviour of the structure in Fig. 3, when a plastic hinge develops at C.

11.        Consider a simply supported girder AB of span l. When a uniformly distributed load of ‘w’ per unit length longer than the span crosses the girder from left to right, construct

(i)            the maximum shear force diagrams

(ii)           the maximum bending moment diagram

Indicate ordinates at any distance x from A.

12.        Answer either (a) or (b)

(a)        A beam ABC is supported at A, B and C as shown in Fig. 7. It has the hinge at D. Draw the influence lines for

(1)   reactions at A, B and C

(2)   shear to the right of B

(3)   bending moment at E

 B
 A
 2m
 8m
 3m
 4m
 C
 E
 D

(b)        Determine the influence line ordinates at any section X on BC of the continuous

beam ABC shown in Fig. 8, for reaction at A.

 5m
 5m
 x
 X
 C
 B
 A

13.        Answer either (a) or (b)

(a)   A parabolic 3 hinged arch shown in fig. 9 carries loads as indicated. Determine

(i)   resultant reactions at the 2 supports                                                              (7)

(ii)  bending moment, shear (radial) and normal thrust at D, 5m from A.      (3+3+3)

 3m
 4m
 3m
 20 kN
 30 kN
 25 kN/m
 C
 B
 A
 20m
 D
 5m
 5m

(b)   A 3 hinged parabolic arch has a horizontal span of 30m and a central rise of 5m. A

point of 10 kN moves over the span.

(i)    Plot the influence line for bending moment at a point 8m from left support.  (6)

(ii)   Find the maximum positive & negative bending moments at this section.  (4)

(iii)  Sketch the absolute maximum bending moment diagrams and show the peak

ordinates and their positions.                                                      (6)

14.        Answer either (a) or (b)

(a)   A suspension bridge with a 2 hinged stiffening girder (fig. 10) has a span of 120m. It

has a central dip of 18m. A live load of 12 kN/m is on the bridge a shown. Find

(i)   the horizontal pull at A and B, due to the live load. (assume that the strain

energy contribution of the cable is negligible). Take EI of the girder as

16 x 105 kNm2.                                                                           (13)

(ii)    What is the purpose served by the stiffening girder? Does it really stiffen the

cable?                                                                                       (3)

 120m
 25 kN/m
 18m
 B
 A
 60m
 30m

(b)  Using the method of tension coefficients determine the forces in the members of a 6

member tetrahedral space frame conforming to the data in Table 1 below:

 No. Node Co-ordinates (m) X Y Z 1. A 0 0 0 2. B 3 4 0 3. C 6 0 0 4. D 3 2 5

At node D (the apex) a downward force of 75 kN acts in the Z direction and a force of 5 kN acts in the X direction. The ground supports are designed to develop the following reactions only.

 A point Reaction directions A Y, Z B X, Z C Y, Z

(i)   Find the 6 reactions                    (10)

(ii)  Find the 6 member forces           (6)

15.        Answer either (a) or (b)

(a)   A curved beam in the form of a quadrant of a circle is fixed at A and free at B

(fig. 11). It carries a downward load of W at the free and

(i)  Find the following values for a section X, at an angular distance q from OB.

i. (a)  Shear force                       (2)

i. (b)  Bending moment               (2)

i. (c)  Twisting moment               (4)

(ii)  Find the deflection at B               (8)

 900
 O
 W
 R
 R
 E,I,G,I
 B
 x
 q
 A

(b)  An RC portal frame is tested in the lab under 2 concentrated loads W, W increasing

of equal magnitude. If Mp=160 kN/m for all members,

(i)   Find the value of W at which the portal would collapse under each of the

mechanisms shown in fig. 12.                                                      (3 x 4)

(ii)  What will be the most likely collapse load?                        (4)

 2m
 2m
 4m
 3m
 3m
 W
 W
 2m
 2m
 4m
 3m
 3m
 W
 W

(a)                                                                                                   (b)

 2m
 2m
 4m
 3m
 3m
 W
 W
 2m
 2m
 4m
 3m
 3m
 W