Instructions:
- The marks are indicated in the right‑hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Assume any data not given.
Q.1 Choose the correct answer of the following (any seven) :
Stiffness matrix method is known as
The degree of kinematic indeterminacy of a two‑bay, three‑storey portal frame fixed at the base is
If three members meet at a joint and the stiffness of the members are $k_{1} = 2EI$, $k_{2} = EI$, $k_{3} = 1.5EI$, then the distribution factor for member 3 is
If the area of $(M / EI)$ diagram between points $A$ and $B$ is -ve, then angle from tangent $A$ to tangent $B$ will be measured
For drawing ILD, what value of test load is assumed?
If all the reactions acting on a planar system are concurrent in nature, then the system is
For stable structures, one of the important properties of stiffness matrix is that the elements on the main diagonal
Which of the following is not the displacement method?
The principle of virtual work can be applied to elastic system by considering the virtual work of
If in ILD analysis peak force comes out to be $2\mathrm{kN}$, then what will be the peak force if loading is $2\mathrm{kN}$ ?
Q.2 Solve this question :
Explain external and internal indeterminacy of structure. What is degree of freedom? Compute ordinates of influence line for moment at mid‑span of PC for the beam (Fig. 1) at 1 m interval (locations 1, 2, 3, 4, 5, 6) and draw influence line diagram. Assume moment of inertia to be constant throughout.
Q.3 Solve this question :
State the assumption of the slope‑deflection equations. Analyse the frame as shown in Fig. 2 by slope deflection method and draw bending moment diagram. Assume El same for all the members.
Q.4 Solve both questions :
Explain moment distribution method. What is meant by distribution factor?
Analyse the continuous beam shown in Fig. 3 by moment distribution method and draw bending moment diagram. Assume El is constant throughout.
Q.5 Solve this question :
State usefulness of three moment equations. Derive the support moments in the continuous beam shown in Fig. 4 by using three moment equations.
Q.6 Solve this question :
Derive moment area theorems. Determine the rotation at supports and deflection at mid‑span and under the loads in the simply supported beam as shown in Fig. 5.
Q.7 Solve this question :
Explain first theorem of Castigliano. Determine the vertical deflection at the free end and rotation at A in the overhanging beam as shown in Fig. 6 using Castigliano's theorem. Assume El constant.
Q.8 Solve both questions :
Determine stiffness matrix and flexibility matrix of a beam and plane.
What do you mean by flexibility and stiffness of a structure? What is the relation between flexibility and stiffness? Analyse the continuous beam shown in Fig. 7 by stiffness matrix method.
Q.9 Solve this question :
State Bernoulli's principle of virtual displacement. Explain cantilever method of analysis of structure. Analyse the frame (Fig. 8) by cantilever method.
Instructions:
- The marks are indicated in the right‑hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Assume any data not given.
Q.1 Choose the correct answer of the following (any seven) :
Stiffness matrix method is known as
The degree of kinematic indeterminacy of a two‑bay, three‑storey portal frame fixed at the base is
If three members meet at a joint and the stiffness of the members are $k_{1} = 2EI$, $k_{2} = EI$, $k_{3} = 1.5EI$, then the distribution factor for member 3 is
If the area of $(M / EI)$ diagram between points $A$ and $B$ is -ve, then angle from tangent $A$ to tangent $B$ will be measured
For drawing ILD, what value of test load is assumed?
If all the reactions acting on a planar system are concurrent in nature, then the system is
For stable structures, one of the important properties of stiffness matrix is that the elements on the main diagonal
Which of the following is not the displacement method?
The principle of virtual work can be applied to elastic system by considering the virtual work of
If in ILD analysis peak force comes out to be $2\mathrm{kN}$, then what will be the peak force if loading is $2\mathrm{kN}$ ?
Q.2 Solve this question :
Explain external and internal indeterminacy of structure. What is degree of freedom? Compute ordinates of influence line for moment at mid‑span of PC for the beam (Fig. 1) at 1 m interval (locations 1, 2, 3, 4, 5, 6) and draw influence line diagram. Assume moment of inertia to be constant throughout.
Q.3 Solve this question :
State the assumption of the slope‑deflection equations. Analyse the frame as shown in Fig. 2 by slope deflection method and draw bending moment diagram. Assume El same for all the members.
Q.4 Solve both questions :
Explain moment distribution method. What is meant by distribution factor?
Analyse the continuous beam shown in Fig. 3 by moment distribution method and draw bending moment diagram. Assume El is constant throughout.
Q.5 Solve this question :
State usefulness of three moment equations. Derive the support moments in the continuous beam shown in Fig. 4 by using three moment equations.
Q.6 Solve this question :
Derive moment area theorems. Determine the rotation at supports and deflection at mid‑span and under the loads in the simply supported beam as shown in Fig. 5.
Q.7 Solve this question :
Explain first theorem of Castigliano. Determine the vertical deflection at the free end and rotation at A in the overhanging beam as shown in Fig. 6 using Castigliano's theorem. Assume El constant.
Q.8 Solve both questions :
Determine stiffness matrix and flexibility matrix of a beam and plane.
What do you mean by flexibility and stiffness of a structure? What is the relation between flexibility and stiffness? Analyse the continuous beam shown in Fig. 7 by stiffness matrix method.
Q.9 Solve this question :
State Bernoulli's principle of virtual displacement. Explain cantilever method of analysis of structure. Analyse the frame (Fig. 8) by cantilever method.
Instructions:
- The marks are indicated in the right‑hand margin.
- There are EIGHT questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer of the following (any seven):
Principle of superposition is applicable when
The Castigliano's second theorem can be used to compute deflections
When a load crosses a through‑type Pratt truss in the direction left to right, the nature of force in any diagonal member in the left half of the span would
For a three‑hinged arch, if one of the supports settles down vertically, then the horizontal thrust
A number of forces acting at a point will be in equilibrium, if
A beam is said to be of uniform strength, if
A load 'W' is moving from left to right supported on simply supported beam of span 'L'. The maximum bending moment at 0·4 L from the left support is
The deformation of a spring produced by a unit load is called
For stable structures, one of the important properties of flexibility and stiffness matrices is
that
the elements on the main diagonal
1. of a stiffness matrix must be positive
2. of a
stiffness
matrix must be negative
3. of a flexibility matrix must be positive
4. of a flexibility
matrix
must be negative
The correct answer is
If kinematic indeterminacy is more than the static indeterminacy, then the method used for solving the structures is
Q.2 Solve both questions :
Describe the differences between static and kinematic indeterminacy. Also determine static and kinematic indeterminacy of structures shown in Fig. 1. What is kinematic indeterminacy if axial deformations are negligible?
Draw the influence line for the bar forces in members $U_{1}U_{2}$, $L_{1}L_{2}$ and $U_{1}L_{2}$ of the truss as shown in Fig. 2. The length of each panel is $5 \mathrm{~m}$ and height of truss is 4.
Q.3 Solve this question :
Four wheel loads $20 \mathrm{kN}$, $80 \mathrm{kN}$, $60 \mathrm{kN}$ and $100 \mathrm{kN}$ spaced at $2 \mathrm{~m}$, $3 \mathrm{~m}$ and $4 \mathrm{~m}$, respectively roll on girder of span $10 \mathrm{~m}$ from left to right with the $100 \mathrm{kN}$ load leading. Find the maximum and absolute maximum bending moment that can occur at a section $4 \mathrm{~m}$ from the left support. Also determine the maximum positive and negative shear forces at that section.
Q.4 Solve both questions :
Determine the reaction at the support and maximum positive and negative bending moment developed in the three hinged circular segment arch. The arch is subject to a concentrated load W at the distance $3 \mathrm{a}$ from left support. The span is of $12 \mathrm{a}$ and rise at crown is $2 \mathrm{a}$.
What is the difference between real work done and virtual work done? Also derive the expression for strain energy due bending of beams.
Q.5 Solve this question :
Find vertical deflection, horizontal deflection and slope at end A of the frame member ABCDE shown in Fig. 3. Take $E = 200 \mathrm{kN} / \mathrm{mm}^2$, $I_{AC} = 6 \times 10^7 \mathrm{~mm}^4$ and $I_{CE} = 7 \times 10^7 \mathrm{~mm}^4$.
Q.6 Solve both questions :
A suspension cable is suspended from two piers $200 \mathrm{m}$ centre‑to‑centre, one support being $5 \mathrm{m}$ above the other. The cable carries a u.d.l. of $15 \mathrm{N} / \mathrm{m}$ and has its lower point $10 \mathrm{m}$ below the lower support. The ends of the cable are attached the saddled on rollers at top of piers. The back stays are inclined at $60^{\circ}$ to the vertical. Determine— (i) the maximum tension in the cable; (ii) tension in the back stays.
A three‑hinged parabolic arch is subjected to u.d.l. of $20 \mathrm{kN} / \mathrm{m}$ throughout its length. Find bending moment, radial shear, normal thrust at a distance $20 \mathrm{m}$ from left support, if the arch has a span of $100 \mathrm{m}$ and rise of $25 \mathrm{m}$.
Q.7 Solve both questions :
A three‑hinged parabolic arch of span $18 \mathrm{m}$ has its left support at depth $5 \mathrm{m}$ and right support at depth $12 \mathrm{m}$ below the crown hinge. The arch carries a point load of $45 \mathrm{kN}$ at a distance of $4 \mathrm{m}$ from left side of crown hinge and point load of $90 \mathrm{kN}$ at a distance of $8 \mathrm{m}$ from right side of the crown hinge. Find the reaction at the supports and the bending moment under the loads.
A beam AB of length $10 \mathrm{m}$ simply supported at the ends carries a point load $100 \mathrm{kN}$ at '4' distance from the left and '6' distance from right end. Find the deflection under the load by conjugate method and draw the shear force and bending moment diagram.
Q.8 Solve both questions :
Show that the flexibility and stiffness matrix are inversely proportional to each other. Generate the stiffness matrix coefficient of structure shown in Fig. 4. EI is constant throughout the span.
Determine the flexibility matrix of the structure shown in Fig. 5. The base width and height of the plane frame is $L$. $EI$ is constant through the structure.
Instructions:
- The marks are indicated in the right‑hand margin.
- There are EIGHT questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer of the following (any seven):
Principle of superposition is applicable when
The Castigliano's second theorem can be used to compute deflections
When a load crosses a through‑type Pratt truss in the direction left to right, the nature of force in any diagonal member in the left half of the span would
For a three‑hinged arch, if one of the supports settles down vertically, then the horizontal thrust
A number of forces acting at a point will be in equilibrium, if
A beam is said to be of uniform strength, if
A load 'W' is moving from left to right supported on simply supported beam of span 'L'. The maximum bending moment at 0·4 L from the left support is
The deformation of a spring produced by a unit load is called
For stable structures, one of the important properties of flexibility and stiffness matrices is
that
the elements on the main diagonal
1. of a stiffness matrix must be positive
2. of a
stiffness
matrix must be negative
3. of a flexibility matrix must be positive
4. of a flexibility
matrix
must be negative
The correct answer is
If kinematic indeterminacy is more than the static indeterminacy, then the method used for solving the structures is
Q.2 Solve both questions :
Describe the differences between static and kinematic indeterminacy. Also determine static and kinematic indeterminacy of structures shown in Fig. 1. What is kinematic indeterminacy if axial deformations are negligible?
Draw the influence line for the bar forces in members $U_{1}U_{2}$, $L_{1}L_{2}$ and $U_{1}L_{2}$ of the truss as shown in Fig. 2. The length of each panel is $5 \mathrm{~m}$ and height of truss is 4.
Q.3 Solve this question :
Four wheel loads $20 \mathrm{kN}$, $80 \mathrm{kN}$, $60 \mathrm{kN}$ and $100 \mathrm{kN}$ spaced at $2 \mathrm{~m}$, $3 \mathrm{~m}$ and $4 \mathrm{~m}$, respectively roll on girder of span $10 \mathrm{~m}$ from left to right with the $100 \mathrm{kN}$ load leading. Find the maximum and absolute maximum bending moment that can occur at a section $4 \mathrm{~m}$ from the left support. Also determine the maximum positive and negative shear forces at that section.
Q.4 Solve both questions :
Determine the reaction at the support and maximum positive and negative bending moment developed in the three hinged circular segment arch. The arch is subject to a concentrated load W at the distance $3 \mathrm{a}$ from left support. The span is of $12 \mathrm{a}$ and rise at crown is $2 \mathrm{a}$.
What is the difference between real work done and virtual work done? Also derive the expression for strain energy due bending of beams.
Q.5 Solve this question :
Find vertical deflection, horizontal deflection and slope at end A of the frame member ABCDE shown in Fig. 3. Take $E = 200 \mathrm{kN} / \mathrm{mm}^2$, $I_{AC} = 6 \times 10^7 \mathrm{~mm}^4$ and $I_{CE} = 7 \times 10^7 \mathrm{~mm}^4$.
Q.6 Solve both questions :
A suspension cable is suspended from two piers $200 \mathrm{m}$ centre‑to‑centre, one support being $5 \mathrm{m}$ above the other. The cable carries a u.d.l. of $15 \mathrm{N} / \mathrm{m}$ and has its lower point $10 \mathrm{m}$ below the lower support. The ends of the cable are attached the saddled on rollers at top of piers. The back stays are inclined at $60^{\circ}$ to the vertical. Determine— (i) the maximum tension in the cable; (ii) tension in the back stays.
A three‑hinged parabolic arch is subjected to u.d.l. of $20 \mathrm{kN} / \mathrm{m}$ throughout its length. Find bending moment, radial shear, normal thrust at a distance $20 \mathrm{m}$ from left support, if the arch has a span of $100 \mathrm{m}$ and rise of $25 \mathrm{m}$.
Q.7 Solve both questions :
A three‑hinged parabolic arch of span $18 \mathrm{m}$ has its left support at depth $5 \mathrm{m}$ and right support at depth $12 \mathrm{m}$ below the crown hinge. The arch carries a point load of $45 \mathrm{kN}$ at a distance of $4 \mathrm{m}$ from left side of crown hinge and point load of $90 \mathrm{kN}$ at a distance of $8 \mathrm{m}$ from right side of the crown hinge. Find the reaction at the supports and the bending moment under the loads.
A beam AB of length $10 \mathrm{m}$ simply supported at the ends carries a point load $100 \mathrm{kN}$ at '4' distance from the left and '6' distance from right end. Find the deflection under the load by conjugate method and draw the shear force and bending moment diagram.
Q.8 Solve both questions :
Show that the flexibility and stiffness matrix are inversely proportional to each other. Generate the stiffness matrix coefficient of structure shown in Fig. 4. EI is constant throughout the span.
Determine the flexibility matrix of the structure shown in Fig. 5. The base width and height of the plane frame is $L$. $EI$ is constant through the structure.