Beam Analysis: Shear and Bending Moment
Introduce internal shear force and bending moment in simple beams and connect external loading to internal actions.
civil Engineering
Professional knowledge base and engineering tools for civil engineering.
Knowledge Categories
Structural Analysis & Design
Beam Bending Stresses
Learn how to calculate the normal stresses within an elastic beam subjected to a bending moment.
Beam Deflection
Learn how to calculate the elastic deflection of simply supported or cantilever beams using the double-integration method.
Calculation Example: Cantilever Beam Shear Force and Bending Moment
Step-by-step calculation example for finding the maximum internal shear force and bending moment in a cantilever beam subjected to a point load at its free end, complete with SFD and BMD.
Calculation Example: Dead and Live Loads
Calculation example for factored area load and total factored floor load using LRFD load combinations
Calculation Example: Degree of Indeterminacy
Worked example for determining the degree of static indeterminacy for coplanar beam structures
Calculation Example: Influence Lines for Determinate Beams
Calculation example for constructing and analyzing influence lines for statically determinate simply supported beams, evaluating support reaction transfer and actual reactions under moving axle loads.
Calculation Example: Truss Analysis by Method of Joints
A calculation example for finding axial forces in a simple truss.
Calculation Example: Wind and Seismic Loads Basics
Calculation example for seismic base shear analysis and lateral force distribution using the Equivalent Lateral Force (ELF) procedure
Concrete Beam Flexure Basics
Foundational concepts for the flexural design of singly reinforced concrete beams.
Concrete Column Design
Design of reinforced concrete short columns under axial load and bending.
Concrete Slab Design Basics
Fundamentals of designing one-way reinforced concrete slabs.
Dead and Live Loads
Foundational definitions and basic combinations of dead and live loads in structural engineering.
Influence Lines for Determinate Beams
Introduction to influence lines for statically determinate beams, tracking how reactions, shear, and moment vary with a moving unit load.
Introduction to Indeterminate Structures
Foundational conceptual framework for differentiating statically determinate and indeterminate structures using equilibrium and compatibility.
Steel Beam Flexural Design
Basic methodology for calculating the nominal flexural strength of steel beams.
Steel Compression Members
Design of structural steel columns focusing on stability and buckling failure modes.
Steel Tension Members Design
Foundational principles of designing structural steel members under axial tension, focusing on yielding and fracture limits.
Stress and Strain — Civil Structural Context
Establish stress and strain in the civil structural context while preserving separation from the generic mechanical treatment.
Truss Analysis
Determine axial forces in idealized planar truss members using the method of joints and static equilibrium.
Wind and Seismic Loads Basics
Foundational concepts of lateral environmental loads on structures.
Worked Example: Beam Bending Stresses
Calculate the maximum bending stress at the outer fibers of a solid rectangular wooden beam.
Worked Example: Concrete Beam Flexure Basics
Calculate the nominal moment capacity (Mn) and design moment capacity (φMn) of a singly reinforced concrete beam per ACI 318 standard.
Worked Example: Steel Tension Members Design
Calculate the design tensile strength of a structural steel member using LRFD for gross and net sections.
Geotechnical Engineering
Calculation Example: Shear Strength of Soils
Worked calculation example for the shear strength of soils using the Mohr-Coulomb failure criterion.
Calculation Example: Soil Consolidation and Settlement
Calculation example for 1-D primary consolidation settlement in normally consolidated clay
Calculation Example: Soil Permeability & Seepage
Worked calculation example determining soil hydraulic conductivity (permeability coefficient, k) using Darcy's Law from a constant-head permeability test.
Normal Stress and Strain — Mechanics of Materials Introduction
Understand normal stress (σ = F/A) and normal strain (ε = δ/L), the foundation of mechanics of materials. Covers axial loading, stress distribution, deformation, and engineering significance, with calculation examples.
Pile Capacity in Deep Foundations
Fundamentals of estimating the ultimate bearing capacity of piles based on soil properties.
Retaining Walls and Lateral Earth Pressure
Geotechnical principles for calculating lateral earth pressures on retaining structures.
Shallow Foundation Bearing Capacity
Foundational concepts for calculating the ultimate bearing capacity of soil for shallow foundations.
Soil Consolidation and Settlement
Foundational principles of primary consolidation and time-dependent settlement in saturated soils.
Soil Permeability & Seepage
Foundational principles of hydraulic conductivity and one-dimensional seepage through soils using Darcy's Law.
Worked Example: Effective Stress in Soils
A comprehensive worked example calculating total stress, pore water pressure, and Terzaghi's effective stress in a saturated clay deposit.
Worked Example: Shallow Foundation Bearing Capacity
Step-by-step calculation of ultimate and allowable bearing capacity for a continuous strip footing using Terzaghi's bearing capacity theory.
Other Topics
Calculation Example: Axial Deformation
An example of calculating the total elongation of a steel rod under an axial tensile force.
Calculation Example: Basic Derivatives
Worked calculation example for basic derivatives, curve slope, and tangent line equations
Calculation Example: Fluid Statics
Calculation example for Fluid Statics Fundamentals
Calculation Example: Normal Stress and Strain — Introduction to Mechanics of Materials
Calculation example for Normal Stress and Strain — Introduction to Mechanics of Materials
Calculation Example: Temperature and Heat Concepts
Calculation example for temperature and heat concepts
Calculation Example: Triangle Area
A calculation example of building gable wall surface area for wind load analysis and architectural material estimation.
Mathematical Functions Graphing
Learn the basics of mathematical functions and interactively plot various graph types.
Second Moment of Area
Understanding the geometric property that dictates a cross-section's resistance to bending.
Worked Example: Basic Area and Volume
A worked example demonstrating the transition from 2D area to 3D volume.
Worked Example: Linear Interpolation
Engineering calculation example for Linear Interpolation to determine physical properties from property tables.
Worked Example: Ratio and Proportion (Scaling Up & Down)
A worked example demonstrating the use of ratio and proportion for engineering scaling, including both enlarging and reducing sizes.
Worked Example: Triangle Geometry & Pythagoras
A worked example demonstrating the use of the Pythagorean theorem in spatial reasoning.