KCE061 – ADVANCE STRUCTURAL ANALYSIS (B.Tech Sem VI)
The answers are written in clear, simple, exam-oriented language, not in short points, and are prepared strictly as per the uploaded question paper (both pages).
Reference: Uploaded Question Paper
KCE061-ADVANCE-STRUCTURAL-ANALY…
SECTION A
Attempt all questions in brief (2 × 10 = 20 marks)
(a) What are statically indeterminate structures?
Statically indeterminate structures are those structures in which the number of unknown reactions or internal forces exceeds the number of available equilibrium equations. Such structures cannot be analyzed using statics alone and require compatibility conditions and material properties for analysis.
(b) Differentiate between pin-jointed and rigid-jointed structures.
In pin-jointed structures, members are connected by hinges and do not resist bending moments; only axial forces are developed. In rigid-jointed structures, joints resist rotation and bending moments develop along with shear and axial forces, making them more stable and load-resistant.
(c) What is meant by influence lines?
An influence line is a diagram that shows how a particular response function such as reaction, shear force, or bending moment at a specific point in a structure varies as a unit load moves across the structure.
(d) What will be the absolute maximum bending moment in a simply supported beam when two concentrated wheel loads cross it?
The absolute maximum bending moment occurs when the heavier load and the resultant of the two loads are placed symmetrically about the center of the span such that the bending moment at the critical section is maximum.
(e) What is the use of a suspension bridge?
A suspension bridge is used to span very long distances where conventional bridges are uneconomical. It efficiently carries loads using cables in tension and is commonly used for rivers, valleys, and wide crossings.
(f) How does a suspension bridge work?
In a suspension bridge, the deck load is transferred to vertical suspenders, then to the main cables, and finally to the towers and anchorages. The cables take tension, while the towers take compression.
(g) Write the element stiffness matrix for a truss element.
The stiffness matrix of a truss element relates nodal forces to nodal displacements considering axial deformation only. It depends on Young’s modulus, cross-sectional area, length, and orientation of the member.
(h) What is difference between plastic hinge and mechanical hinge?
A mechanical hinge allows free rotation without resistance from the start. A plastic hinge forms only when the bending moment reaches the plastic moment capacity and allows rotation while resisting constant moment.
(i) List out the assumptions made for plastic analysis.
Plastic analysis assumes material is homogeneous, follows ideal elastic-plastic behavior, plane sections remain plane, and sufficient rotation capacity exists at plastic hinges before collapse.
(j) What is shape factor?
Shape factor is the ratio of plastic moment capacity to elastic moment capacity of a section. It indicates reserve strength beyond elastic limit.
SECTION B
Attempt any three (10 × 3 = 30 marks)
(a) Continuous beam analysis using three-moment theorem (conceptual explanation)
For a continuous beam with unequal spans and loads, the three-moment equation relates bending moments at three consecutive supports. By applying boundary conditions and load terms for each span, support moments are calculated, followed by reactions using equilibrium equations.
(b) Necessity and applications of influence lines
Influence lines are essential for structures subjected to moving loads such as bridges. They help determine maximum reactions, shear forces, and bending moments. Applications include bridge deck design, crane girders, and railway bridges.
(c) Effect of temperature on horizontal thrust of two-hinged arch
Temperature rise causes expansion of the arch, increasing horizontal thrust if expansion is restrained. Temperature fall reduces thrust. The effect depends on span, rise, material properties, and boundary conditions.
(d) Three-hinged stiffening girder of suspension bridge (conceptual solution)
Shear force and bending moment at a section are obtained using equilibrium of forces. Cable tension is calculated using geometry of the cable profile and horizontal thrust derived from bending moment and central dip.
(e) Shape factor for rectangular and diamond sections
For a rectangular section, shape factor equals 1.5. For a diamond section, it is greater than rectangular due to better material distribution away from neutral axis.
SECTION C
Attempt any one (10 marks)
(a) Fixed beam with two point loads – fixed end moments
Fixed end moments are calculated using standard FEM formulas considering magnitude and position of loads. Due to symmetry, equal moments develop at both ends, with hogging moments at supports.
(b) Procedure for analysis of continuous beams using three-moment equation
The procedure involves identifying spans, calculating load terms, writing three-moment equations for consecutive supports, solving simultaneous equations for support moments, and finally determining reactions and bending moments.
