1010234110

  Mechanics of Structures  

                                                                        Theory 
                         UNIT I SLOPE AND DEFLECTION OF BEAMS
Deflected shapes / Elastic curves of beams with different support conditions –
Definition of Slope and Deflection- Flexural rigidity and Stiffness of beams- Mohr’s
Theorems – Area Moment method for slope and deflection of beams – Derivation of
expressions for maximum slope and maximum deflection of standard cases by area
moment method for cantilever and simply supported beams subjected to symmetrical
UDL& point loads.
Numerical problems on determination of slopes and deflections at salient points of
Cantilever Beam with maximum two point loads, udl throughout the beam, udl for the
half length from fixed end and Combination of single point load and udl throughout
the beam only- Determination of slopes and deflections at salient points of Simply
supported beams with central point load, Two equal point loads at one third points,
udl throughout the beam and Combination of central point load and udl throughout
the beam only from first principles and by using formulae.

 UNIT II FIXED BEAMS–AREA MOMENT METHOD

Introduction to fixed beam – Advantages –Degree of indeterminacy of fixed beam-
Sagging and Hogging bending moments- Points of Contra flexure. – Determination

of fixing end(support) moments(FEM) by Area Moment method– Bending moment
diagram(BMD)-Free BMD –Fixed BMD- Derivation of Expression for subjected to
concentrated load at mid span, Single eccentric point load, udl throughout the beams.
Numerical Problems for Fixed beams subjected to concentrated load at mid span,
Single eccentric point load, Two equal point loads at one third points, udl throughout
the beams, Combination of central point load and udl throughout the beam only.
Drawing SF and BM diagrams for Fixed beams with supports at the same level (sinking
of supports or supports at different levels are not included)

UNIT III CONTINUOUS BEAMS–THEOREM OF THREE MOMENTS METHOD

Introduction to continuous beams-Advantages–Deflected shapes of continuous
beam-Degree of indeterminacy of continuous beams with respect to number of spans
and types of supports –Simple/ Fixed supports of beams- General methods of
analysis of Indeterminate structures – Clapeyron’s theorem of three moments–
Application of Clapeyron’s theorem of three moments for the following cases–Two
span beams with both ends simply supported –Two span beams with one end fixed
and the other end simply supported.
Numerical Problems on Two span beams with both ends simply supported –Two span
beams with one end fixed and the other end simply supported -Sketching of SFD and
BMD for all the above cases.

    UNIT IV PORTAL FRAMES – MOMENT DISTRIBUTION METHOD

Introduction to moment distribution method- Carry over moment-Carryover factor and
Stiffness factor (Derivation not required)-Distribution moment- Distribution factor—
Stiffness Ratio or Relative Stiffness- Concept of distribution of un balanced moments
at joints – Sign conventions,
Definition of Frames– Types–Bays and Story – Sketches of Single/Multi Story Frames,
Single/Multi Bay Frames- Portal Frame– Sway and Non- sway Frames- Deflected
shapes of Portal frames under different loading / support conditions- Numerical
problems of Non sway (Symmetrical) Portal Frames for Joint moments by Moment
Distribution Method and drawing BMD only.

   UNIT V COLUMNS AND STRUTS

Columns and Struts–Definition–Short and Long columns–End conditions –
Equivalent length / Effective length– Slenderness ratio – Axially loaded short column
– Axially loaded long column – Euler’s theory of long columns-Assumptions –
Expression for Critical load of Columns standard cases of end conditions-Limitations

of Euler’s formula – Modes of failure of column-Buckling of column-Buckling load-
crushing load-safe load- Factor of Safety– Expression of Rankine’s formula for

Crippling load of Columns – Simple problems for circular column, Hollow circular
column, Rectangular column, Single I section without cover plate only.