Bending_2ndPart

Structural loads

Structural loads are the forces and moments applied to the structure. They are further divided into following types:

1. Surface loads  ↔  externally applied load on the surface (like point load, line load, pressure, bending, torsion).
2. Body loads  ↔  developed internally within the structure (gravity, weight, thermal load).

There are other types of loads with respect to time:

1. Static load  ↔  if load is not a function of time (have constant magnitude, directions and location).
2. Dynamic load  ↔  if load is a function of time.
3. Quasi-Static load  ↔  if load varies slowly with time (taken as static load).

Dynamic loads are further divided as follows:

1. Steady-State loads  ↔  which maintain same character (like frequency, amplitude, etc) over the long term.
2. Transient loads  ↔  which change their character with time.

Taxonomy of Structure

Classification of structures (complex systems) by decomposing them into their simpler parts (structural elements). It is divided into 2 types:

1. Line Forming Elements (mostly beam)
2. Surface Forming Elements (Area and Volume Forming)

Determinancy of System

Determinancy of system is defined as, "if no. of unknowns is equal to the no. of equations".

• If few constraints (less supports) than required  ↔  structure is under-constraints and unstable.

i =  m  +  r  -  2( j ) 

Modelling and Analysis

The characteristics tasks in Structural analysis are:

• Supports structural design
• Understanding the complex response 
• Resultant stress and strain
• Displacement to applied loads which gives strength and stiffness

The method of Structural analysis (Mathematical & Experimental analysis) involves 3 parts:

• Equilibrium  ↔  if body is in global equilibrium, every local particle is in equilibrium.
• Static analysis  ↔  implies negligible acceleration
• Dynamic analysis  ↔  motion of body including inertial forces
• Deformation  ↔  geometry of material displacement, strain (assuming continuous material, fully populated with particles) and Linear analysis (small displacement).
• Constitution  ↔  Stress and strain are intimately related to given material (or structural) system

Experimental Analysis involves:

• Testing of real (or prototypical) structural techniques for strain.
• Instruments: Extensometer, strain gages, optical interferometer, etc.

For bending phenomena   ↔  click here

Combine Loading

To solve combination of bending and longitudinal load applied to member we use Method of Superposition.

• Column is not just below the member but it is at a distance (eccentric) by means of bracket.
• Resultant Combine loading stresses  =  Direct stress  +  Bending stress

Eccentric End Loading

If end load 'P' does not act at the centroid of cross section, then it will setup bending moments about the principal axes.

• Application  ↔  used in Civil engineering where short concrete beams are subjected to a compressive load which may be eccentric.

Importance of Section Modulus

Section Modulus is defined as, "the ratio of Moment of Inertia to Distance of Outer fiber from Neutral Axis".

• Depends only on the geometry of the cross-section.
• Higher value of section modulus  ↔  Lesser beam failure chance.
• Large values of ratio Height 'd' and Breadth 'b'  ↔  results in Lateral Instability of the beams.
• Wide-flange steel beams are used in the frame of the building.

Asymmetric or Skew Bending of the Beam

Symmetric Bending assumptions:

1. Beam section is symmetric about the deflection axis 
2. Beam material has the same Tensile or Compressive stiffness.

Asymmetric Bending:

• Bending in Y and Z axis simultaneously

Steps to find Bending Stress:

1. Find IZ and IY.
2. Find MZ and MY.
3. Inspection which corner will have the max. tensile stresses and max. compressive stresses.
4. Calculate the bending stress at the four corners.
5. Find the orientation of the Neutral Axis.

References:

• Material from Class Lectures + Book named Engineering Mechanics of Materials by R.C. Hibbeler (6/9th Edition) + my knowledge. 
• Pics and GIF from Google Images.  
• Videos from YouTube (Engineering Sights).