Shear Force and Bending Moment

By: Mehdizadeh Kabuli

Shear Force and Bending Moment as Structural Basics

Basic structural learning begins with an analyzing of a simply supported beam. A beam is a structural member (horizontal) that is design to support the applied load (vertical). It resists the applied loading by a combination of internal transverse shear force and bending moment. An accurate analysis required in order to make sure the beam is construct without any excessive loads which affect its strength.

Types Of Load and Support

Two types of typical loadings:

Concentrated load is one which can be considered to act at a point although of course in practice it must be distributed over a small area (normally vertical or incline loads). (Unit in kN)

Distributed load is one which is spread in some manner over the length or a significant length of the beam. It is usually quoted at a weight per unit length of beam and it may either be uniform or varying loading from point to point. (Unit in kN/m)

Three types of support:

Namely as Pinned support, Roller support and Fixed or Built-in support.
Covered in previous post together the reactions explained in diagrams.[*]

Reinforced concrete analysis

By: Mehdizadeh Kabuli

Reinforced concrete analysis is performed at a given section for either axial force and bending moment or transverse shear loads. The axial force and bending moment analysis usually idealizes the stress-strain behavior of the concrete with a rectangular stress block to simplify the calculations. More detailed, moment curvature analysis may be performed with more complex stress-strain relationships.

Reinforced Concrete Analysis Types:

• Axial Force and Bending Moment
  
  • Pure flexure design example
    
• Moment Curvature Analysis
  
  

[↑] Axial Force and Bending Moment:

Reinforced concrete analysis for axial force and bending moment is usually performed by assuming a given strain value at the extreme compression fiber with a linear strain distribution over the depth of the section. The stress distribution typically assumes a rectangular stress block with a depth equal to some fraction of the neutral axis depth and a magnitude equal to some fraction of the concrete compressive strength.[*]



Design Parameters:

a. Stress and strain

Depth to neutral axis = c

Maximum concrete strain = ε

Concrete compressive strength = ƒ'_c

Reinforcing yield strength = ƒ_y

b. Stress block

Ratio of average concrete stress = α₁

Ratio of stress block depth = β₁

c. Reduction factors (American, ACI 318)

Reinf reduction factor for tension and flexure = ф

Reinf reduction factor for comp and flexure = ф

Note: Strength reduction factors are used in the American codes, both ultimate strength design and load-resistance factor design. These factors are applied to the computed strength based on the mode of failure.

d. Resistance factors (Canadian, CSA A23.3)

Concrete resistance factor = ф_c

Reinforcement resistance factor = ф_r

Note: Resistance factors are used in the Canadian codes and are applied directly to the material strengths without regard to the mode of failure.

Notation

By Ing. M. R. Mehdi (Mehdizadeh Kabuli)

The basis of the notation adopted in this weblog is that employed in BS8110 and CP110.

Ac	Area of concrete
Ac1	Area of core of helically reinforced column
As	Area of tension reinforcement
A's	Area of compression reinforcement
A's1	Area of compression reinforcement near more highly compressed column face
As2	Area of reinforcement near less highly compressed column face
Asc	Total area of longitudinal reinforcement (in columns)
Ash	Equivalent area of helical binding (volume per unit length)
Asl	Area of longitudinal reinforcement provided for torsion
As prov	Area of tension reinforcement provided
Asreq	Area of tension reinforcement required
Asv	Cross-section area of two legs of link reinforcement
δAs	Area of individual tension bar
δA's	Area of individual compression bar
Atr	Transformed concrete area
a	Dimension (as defined); deflection
ab	Distance between centers of bars
ac	Distance to centroid of compression reinforcement
at	Distance to centroid of tension reinforcement
b	Width of section; dimension (as defined)
bt	Breadth of section at level of tension reinforcement
bw	Breadth of web or rib of member
C	Torsional constant
cmin	Minimum cover to reinforcement
D	Density (with appropriate subscripts)
Dc	Density (i.e. unit weight) of concrete at time of test
d	Effective depth to tension reinforcement
d'	Depth to compression reinforcement
dmin	Minimum effective depth that can be provided
d1	Diameter of core of helically bound column
dc	Depth of concrete in compression (simplified limit-state formulae)
Ec	Static secant modulus of elasticity of concrete
Es	Modulus of elasticity of steel
e	Eccentricity; dimension (as defined)
ea	Additional eccentricity due to deflection in wall
ex	Resultant eccentricity of load at right angles to plane of wall
ex1	Resultant eccentricity calculated at top of wall
ex2	Resultant eccentricity calculated at bottom of wall
F	Total load
Fb	Tensile force due to ultimate load in bar or group of bars
Fh	Horizontal component of load
Ft	Tie force
Fv	Vertical component of load

Contents

By Ing. M. R. Mehdi

Preface
The authors
Notation
Introduction
Safety factors
Loads
Pressures and Stresses
Structural analysis
Materials
Resistance of structural members
Fram analysis
Joints and intersections between members
Resistance to shearing and torsional forces
Beams
Slabs
Arches
Columns
Walls
Foundations