Structural Analysis—I

In case of conjugate beam the internal hinged is converted into which support?

The ordinates of influence line diagram for bending moment always have dimension of

A three‑hinged parabolic arch of span 20 and rise 5 carries UDL of intensity 15 kN/m over whole span, the value of bending moment at a section 5 m from left end is

Flexibility matrix method is based on the

In a simply supported beam, a load $20 \mathrm{kN}$ is placed at $A$ which is at a distance of $6 \mathrm{m}$ from the left caused the deflection at $B$ of $10 \mathrm{mm}$. When the load is $10 \mathrm{kN}$ at $B$ which is same distance from the right end, then find the deflection at point $A$.

The Castigliano's theorem is applicable for the structures

The degree of kinematic indeterminacy of a pin‑jointed space frame is given by

The rate of change of bending moment in any structure is equal to the

A cantilever beam of span $L$ carries point load of intensity $W \mathrm{kN}$ at the free end and another beam which is simply supported at both ends of length $L$ carries point load $W \mathrm{kN}$ at the center. What is the ratio of maximum deflection of cantilever beam to simply supported beam?

The strain energy stored in the member due to bending per unit volume is given by

Describe the differences between determine and indeterminate structures. Also determine static and kinematic indeterminacy of structures shown in Fig. 1.

A three‑hinged parabolic arch ACB of span $30\mathrm{m}$ has its left support at depth $4\mathrm{m}$ and right support at depth $16\mathrm{m}$ below the crown hinge C. The arch carries a point load of $60\mathrm{kN}$ at a distance of $5\mathrm{m}$ from left side of C and point load of $120\mathrm{kN}$ at a distance of $10\mathrm{m}$ from right side of C. Find the reaction at the supports and the bending moment under the loads.

Three wheel loads $60\mathrm{kN}$, $40\mathrm{kN}$ and $50\mathrm{kN}$ spaced at $2\mathrm{m}$ and $2\mathrm{m}$ respectively roll on girder of span $20\mathrm{m}$ from left to right with the $60\mathrm{kN}$ load leading. Find maximum and absolute maximum bending moment that can occur at a section $6\mathrm{m}$ from the left support. Also determine maximum positive and negative shear force at that section.

Find out horizontal and vertical deflections of point A of circular structure shown in Fig. 2, EI is constant :

Derive and describe the Maxwell law of reciprocal deflection theorem and also its generalized form.

A beam AB of length $L$ simply supported at the ends carries a point load $W$ at a distance from the left end and b distance from right end. Find the deflection under the load and the maximum deflection.

A three‑hinged parabolic arch ACB of span $30\mathrm{m}$ has its left support at depth $4\mathrm{m}$ and right support at depth $16\mathrm{m}$ below the crown hinge C. The arch carries a point load of $60\mathrm{kN}$ at a distance of $5\mathrm{m}$ from left side of C and point load of $120\mathrm{kN}$ at a distance of $10\mathrm{m}$ from right side of C. Find the reaction at the supports and the bending moment under the loads.

Find the forces in each member by method of tension coefficient of the Fig. 3 :

A cable is supported between two points $40 \mathrm{m}$ horizontal apart. The left support is $5 \mathrm{m}$ above the right support. The cable carries a load of $6 \mathrm{kN / m}$ on the horizontal span. The lowest point of cable is $5 \mathrm{m}$ below the left support. Find the maximum tension in the cable.

Draw the influence line diagram of the structure as shown in Fig. 4 for reaction at $A$, reaction at $B$, shear force and bending moment at section $E$. Also find the ordinates of influence line diagrams.

Find vertical deflection, horizontal deflection and slope at end $A$ of the frame member ABCD shown in Fig. 5. Take $E = 210 \mathrm{kN / mm^2}$, $I_{AC} = 4 \times 10^7 \mathrm{mm^4}$ and $I_{CD} = 8 \times 10^7 \mathrm{mm^4}$.

What is the difference between flexibility matrix and stiffness matrix? Discuss in detail.

Determine the stiffness matrix of the structure shown in Fig. 6 :

In case of conjugate beam the internal hinged is converted into which support?

The ordinates of influence line diagram for bending moment always have dimension of

A three‑hinged parabolic arch of span 20 and rise 5 carries UDL of intensity 15 kN/m over whole span, the value of bending moment at a section 5 m from left end is

Flexibility matrix method is based on the

In a simply supported beam, a load $20 \mathrm{kN}$ is placed at $A$ which is at a distance of $6 \mathrm{m}$ from the left caused the deflection at $B$ of $10 \mathrm{mm}$. When the load is $10 \mathrm{kN}$ at $B$ which is same distance from the right end, then find the deflection at point $A$.

The Castigliano's theorem is applicable for the structures

The degree of kinematic indeterminacy of a pin‑jointed space frame is given by

The rate of change of bending moment in any structure is equal to the

A cantilever beam of span $L$ carries point load of intensity $W \mathrm{kN}$ at the free end and another beam which is simply supported at both ends of length $L$ carries point load $W \mathrm{kN}$ at the center. What is the ratio of maximum deflection of cantilever beam to simply supported beam?

The strain energy stored in the member due to bending per unit volume is given by

Describe the differences between determine and indeterminate structures. Also determine static and kinematic indeterminacy of structures shown in Fig. 1.

A three‑hinged parabolic arch ACB of span $30\mathrm{m}$ has its left support at depth $4\mathrm{m}$ and right support at depth $16\mathrm{m}$ below the crown hinge C. The arch carries a point load of $60\mathrm{kN}$ at a distance of $5\mathrm{m}$ from left side of C and point load of $120\mathrm{kN}$ at a distance of $10\mathrm{m}$ from right side of C. Find the reaction at the supports and the bending moment under the loads.

Three wheel loads $60\mathrm{kN}$, $40\mathrm{kN}$ and $50\mathrm{kN}$ spaced at $2\mathrm{m}$ and $2\mathrm{m}$ respectively roll on girder of span $20\mathrm{m}$ from left to right with the $60\mathrm{kN}$ load leading. Find maximum and absolute maximum bending moment that can occur at a section $6\mathrm{m}$ from the left support. Also determine maximum positive and negative shear force at that section.

Find out horizontal and vertical deflections of point A of circular structure shown in Fig. 2, EI is constant :

Derive and describe the Maxwell law of reciprocal deflection theorem and also its generalized form.

A beam AB of length $L$ simply supported at the ends carries a point load $W$ at a distance from the left end and b distance from right end. Find the deflection under the load and the maximum deflection.

A three‑hinged parabolic arch ACB of span $30\mathrm{m}$ has its left support at depth $4\mathrm{m}$ and right support at depth $16\mathrm{m}$ below the crown hinge C. The arch carries a point load of $60\mathrm{kN}$ at a distance of $5\mathrm{m}$ from left side of C and point load of $120\mathrm{kN}$ at a distance of $10\mathrm{m}$ from right side of C. Find the reaction at the supports and the bending moment under the loads.

Find the forces in each member by method of tension coefficient of the Fig. 3 :

A cable is supported between two points $40 \mathrm{m}$ horizontal apart. The left support is $5 \mathrm{m}$ above the right support. The cable carries a load of $6 \mathrm{kN / m}$ on the horizontal span. The lowest point of cable is $5 \mathrm{m}$ below the left support. Find the maximum tension in the cable.

Draw the influence line diagram of the structure as shown in Fig. 4 for reaction at $A$, reaction at $B$, shear force and bending moment at section $E$. Also find the ordinates of influence line diagrams.

Find vertical deflection, horizontal deflection and slope at end $A$ of the frame member ABCD shown in Fig. 5. Take $E = 210 \mathrm{kN / mm^2}$, $I_{AC} = 4 \times 10^7 \mathrm{mm^4}$ and $I_{CD} = 8 \times 10^7 \mathrm{mm^4}$.

What is the difference between flexibility matrix and stiffness matrix? Discuss in detail.

Determine the stiffness matrix of the structure shown in Fig. 6 :