Structures with Prof. H

This video presents an example problem for calculating the immediate live load deflections of a reinforced concrete beam according to ACI 318-19. The effective moment of inertia for the beam, which has changed in the most recent version of the code, is computed for dead only and dead + live loading. The service-load displacements are computed, and then the appropriate ACI 318-19 deflection limit is checked. Studying for the FE or PE exams? Save 15% on exam prep materials: - FE Civil: https://ppi2pass.com/fe-exam/civil?affiliate=50524f4648 - PE Civil (Structural): https://ppi2pass.com/pe-exam/civil/structural-depth?affiliate=50524f4648 - PE Civil (Breadth): https://ppi2pass.com/pe-exam/civil/breadth?affiliate=50524f4648 Chapters: 0:00 Introduction 0:34 Serviceability 1:26 Beam Stiffness 3:51 Permissible Deflections 4:57 Example Problem 6:04 Step 1 - Uncracked Section 7:52 Step 2 - Cracked Section 13:42 Step 3 - Effective Moment of Inertia 17:07 Step 4 - Deflections 19:26 Step 5 - Check Permissible

On Tuesday, March 14, the roof collapsed on the Miller Hill Mall in Duluth, Minnesota, under snow loading. How much snow did that roof carry at collapse, and what are the current design standards for computing the flat roof snow load? This video shows an example of how to compute the flat roof snow load prescribed by ASCE/SEI 7-22. Exposure and thermal factors are discussed, as is use of the ASCE 7 Hazard Tool for estimating ground snow loads throughout the United States. This design value is compared to an estimate of how much snow was carried by the Miller Hill at the time of collapse. ASCE 7 Hazard Tool: https://asce7hazardtool.online Studying for the FE or PE exams? Save 15% on exam prep materials: - FE Civil: https://ppi2pass.com/fe-exam/civil?affiliate=50524f4648 - PE Civil (Structural): https://ppi2pass.com/pe-exam/civil/structural-depth?affiliate=50524f4648 - PE Civil (Breadth): https://ppi2pass.com/pe-exam/civil/breadth?affiliate=50524f4648

This video presents a complete example problem for conducting the shear design of reinforced concrete beams according to ACI 318-19. First, the demands are computed using a shear envelope. Then the proper shear limits are checked to ensure the beam dimensions are allowable and that the proper stirrup spacing is selected. Finally stirrup spacing is computed along the length of the beam to satisfy the shear demands. Studying for the FE or PE exams? Save 15% on exam prep materials: - FE Civil: https://ppi2pass.com/fe-exam/civil?affiliate=50524f4648 - PE Civil (Structural): https://ppi2pass.com/pe-exam/civil/structural-depth?affiliate=50524f4648 - PE Civil (Breadth): https://ppi2pass.com/pe-exam/civil/breadth?affiliate=50524f4648 Chapters: 0:00 Introduction 1:16 Shear Envelope 5:50 Concrete Capacity Vc 7:40 Shear Limits 9:15 Minimum Shear Steel 11:09 Capacity with Min Steel 12:20 Required Stirrup Spacing 14:10 Solution

I constructed six reinforced concrete beams in the lab and then loaded them to failure. What can we learn about reinforced concrete behavior and good design principles from these tests? Two of the beams exhibited flexural failures with lots of flexural cracking and ultimate crushing of the concrete in compression. Two beams had traditional shear failures, with a diagonal crack extending through the section. Finally, two beams had anchorage failures, where the ends of the bars pulled out at the support. Good beam design encourages flexural failures because of its ductility and predictability. Chapters: 0:00 Beam Fabrication 0:49 Test Setup 1:23 Beam 1 Test 2:31 Beam 2 Test 3:28 Beam 3 Test 4:19 Beam 4 Test 5:31 Beam 5 Test 6:23 Beam 6 Test 7:03 Results 8:15 Lessons Learned

Shear capacity of reinforced concrete beams has changed from ACI 318-14 to the latest code edition, ACI 318-19. The detailed method is no more, and significant changes have been made the concrete term Vc. This video gives an overview of shear in reinforced concrete beams, highlights the changes in the concrete Vc term, and reviews the steel stirrup contribution Vs. Two example problems are completed: the first for a beam with less than minimum transverse reinforcement, and the second for a beam with more than the minimum transverse reinforcement. Studying for the FE or PE exams? Save 15% on exam prep materials: - FE Civil: https://ppi2pass.com/fe-exam/civil?affiliate=50524f4648 - PE Civil (Structural): https://ppi2pass.com/pe-exam/civil/structural-depth?affiliate=50524f4648 - PE Civil (Breadth): https://ppi2pass.com/pe-exam/civil/breadth?affiliate=50524f4648 Chapters: 0:00 Introduction 2:40 Concrete Vc 6:08 Steel Vs 7:57 Example 1 11:31 Example 2

In this tutorial, we learn how to use ETABS, a structural analysis and building design software package. ETABS has a lot to offer, so this video focuses on learning the basics of how to define a model, apply loads and load combinations, and interpret the analysis results. We first define material and section properties. Then we draw the two-dimensional truss model. Finally, we place point and distributed loads and analyze the deflections, reactions, and axial force and moment diagrams. Chapters: 0:00 Introduction 0:46 Welcome to ETABS 2:00 Navigating Views 3:33 Materials and Sections 5:30 Drawing the Structure 8:33 Modifying the Frames 11:06 Boundaries and Restraints 12:17 Load Patterns and Combinations 15:25 Applying Loads 19:33 Analysis and Results

Learn how to find the required amount of steel to carry the moment demand in a reinforced concrete beam. This video presents two different methods for estimating the steel area: a ballpark method, and a more exact stress ratio method. After introducing these principles, a full design example problem is shown. ACI 318-19 provisions are all satisfied for the minimum area of steel, bar spacing, and beam width. Download Useful Rebar Tables: https://drive.google.com/file/d/1VbndQkIw3vO2jSyv0a1VrpfcYFFKyegE/view?usp=sharing Chapters: 0:00 Introduction 0:30 Beam Design Principles 1:30 Ballpark Method 5:02 Stress Ratio Method 8:12 Example - Demands 9:55 Example - Ballpark Area 12:07 Example - Stress Ratio Area 14:34 Example - Select Steel 16:07 Example - Check Capacity

Wind loads on buildings, showing windward pressure, roof uplift, and leeward suction (outward pressure). #shorts #engineering #structuralengineering

The nominal moment capacity of a concrete beam can be calculated using the Whitney Stress Block approximation (also known as the Equivalent Rectangular Stress Block). This is done to average the nonlinear concrete stresses at the ultimate state. This video also shows how to find the curvature, steel strain, and strength-reduction (phi) factor. Chapters: 0:00 Intro 1:01 Derivation of Capacity 5:44 Strains and Curvature 8:43 Example

Once a reinforced concrete beam is cracked, the section reduces dramatically from the gross moment of inertia to the cracked moment of inertia. This cracked section is active from the cracking moment up until the yielding moment, when the steel yields. Computing the cracked moment of inertia is important for finding deflections of concrete beams under service loads.

In this video, we focus on the first uncracked phase of bending in a reinforced concrete beam. We compute the cracking moment and curvature and cracking using two different approximations: (1) Gross section - ignore the steel, use concrete only (2) Transformed section - transform the steel area into equivalent concrete area The gross section approximation is often used in design, as it is close enough and conservative, but the transformed section may give a more accurate solution. Chapters: 0:00 Flexure in RC 0:41 Gross vs Transformed 2:30 Gross Discussion 5:54 Gross Example 10:56: Transformed Discussion 14:17 Transformed Example

Concrete and steel reinforcement combine into reinforced concrete, one on the most popular building systems on the planet. What makes these materials such a dynamic duo? In this video, we learn about the stress-strain properties of concrete and steel, and why they complement each other. We then see how longitudinal reinforcement helps carry moments and transverse reinforcement (stirrups) helps carry shear in reinforced concrete beams. Finally, we progress through the loading stages of a concrete beam, starting uncracked, then cracked, and finally the yield plateau to failure. Chapters: 0:00 Material Properties 2:42 RC Beam Reinforcement 5:30 Moment Curvature Response

Buildings carry lateral (i.e., horizontal) loads through lateral force resisting systems. This video introduces the three most common systems: (1) Braced frames (2) Moment frames (3) Shear walls The lateral force resisting system does not need to cover the entire structural system, but lateral loads do need to be able to transfer from their point of application to the LFRS. Chapters: 0:00 Introduction 0:55 Braced Frames 2:09 Moment Frames 3:18 Shear Walls 4:28 Outro

This video is the first in a series on approximate structural analysis. Approximate analysis is valuable for checking results from an indeterminate or computer analysis. It is also very useful for multiple choice exams, such as the FE and PE exams - getting a quick answer that is close enough can eliminate incorrect solutions or even hone in on the correct answer. This first video focuses on indeterminate beam analysis. An indeterminate system is converted to a determinate system by adding hinges at the inflection points (i.e., the locations of zero moment). Principles of locating inflection points are discussed, and two full examples problems are shown.

This video illustrates the process for conducting the Direct Analysis Method for steel structures per the 15th Edition of the AISC Steel Construction Manual (AISC 360-16, Specifications for Structural Steel Buildings, Chapter C). This video performs design according to LRFD, though the ASD procedure is similar. The primary benefit of performing structural analysis per the Direct Analysis Procedure is that the effective length factors K for all columns can be assumed equal to 1. Thus, the effective column length is equal to the unbraced length. The necessary features for the Direct Analysis Method are: 1) Stiffness Reductions: apply 80% stiffness to all stiffnesses that contribute to the stability of the structure, plus an additional reduction to flexural stiffness of members with high compressive loads. 2) Second-Order Analysis: consider both P-Delta (capital Delta, accounting for deflections at column ends) and P-delta (lowercase delta, accounting for deflections along the lengths of columns) effects. 3) Notional Loads: lateral loads that account for structural imperfections, equal to 0.002 times the factored gravity loads on each story.

In this video, we derive and apply the slope-deflection equations, which then can be used to find the end moment and end forces on any segment of beam given the rotations, displacements, and loading on that beam. The slope-deflection method forms the basis for so-called "stiffness methods" of structural analysis, wherein the primary unknowns are the displacements and rotations rather than the forces. Using equilibrium, we solve for the unknown displacements and rotations, and then we compute the forces and moments using these deformations. Two examples are conducted. The first example uses the base slope-deflection equations, whereas the second example illustrates what happens when there are locations of zero moment or cantilevers Fixed-end moments, which represent the loading along the beam, are tabulated for many common load cases. I like this version by Prof. Erochko at Carleton University (CC BY-NC-SA 3.0): https://learnaboutstructures.com/sites/default/files/images/15-Appendix/Fixed-End-Moment-Table.pdf

Learn how to calculate the reaction forces for indeterminate structures using the Force Method (sometimes called the flexibility method). The force method is an intuitive way of computing reactions for systems with low degrees of indeterminacy. Supports are removed until the resulting structure is determinate, and then forces are applied at the removed supports to ensure that the displacements at those locations are zero, thereby satisfying the original constraints. These external forces are equivalent to the reaction forces. For the two examples conducted here, the necessary displacements are available from common deflection tables. However, for more complex problems, the setup for the force method lends itself nicely to using the principle of virtual work (PVW) to find all the displacements. See here for how to compute displacements using PVW: https://youtu.be/JAD-8ATyu6k

Learn how to calculate the deflection of a beam using the Moment-Area Method! We define the basic theorems and equations first, and then follow up with two example problems. The curvature of a beam is proportional to the moment, and the curvature is the second derivative of the displacement, so we should be able to use double integration to solve for the displacement. While that works, sometimes it's easier to consider the areas or (for the second integral) the moment of that area to compute displacements. Thus, the Moment-Area method!

In this video tutorial, we learn how to calculate the deflection of a frame or beam using the Principle of Virtual Work. Also known as the Unit Load Method, this basis of this method is two analyze two structures: (1) Real System - The structure with the design loads applied. (2) Virtual System - The structure with a single load of magnitude one applied at the location where deflection is being calculated. We combine the results of these two analyses by balancing out the external and internal work (i.e., strain energy) to compute the deflection of the frame at the location of interest. In general, we can combine the deflection contributions from axial, shear, and moment demands. In practice, the moment dominates the deflections of most beams. Shear is important only for very deep beams, and axial may be important in structures with slender columns or very large axial loads.

In this video tutorial, we learn how to calculate the deflection of a truss using the Principle of Virtual Work. Also known as the Unit Load Method, this basis of this method is two analyze two structures: (1) Real System - The structure with the design loads applied. (2) Virtual System - The structure with a single load of magnitude one applied at the location where deflection is being calculated. We combine the results of these two analyses by balancing out the external and internal work (i.e., strain energy) to compute the deflection of the truss at the location of interest. For more information on conducting truss analysis, see: Truss Analysis - https://youtu.be/Aoj-Hgx45Bo

A design envelope provides the worst-case shear and moment demands along the length of a structure for a suite of load scenarios. In this video, we examine the combination of a static dead load, a patterned (distributed) live load, and a single movable point load. We use the influence lines to find the critical load patterns and positions for the live load. The effect of a distributed load is equal to the magnitude of that distributed load multiplied by the area under the influence line, while the effect of a point load is simply the magnitude of the load multiplied by the value of the influence line at the location of the load. These previous videos show how to compute the influence line (pre-requisite for this video): Influence Lines (statics method) - https://youtu.be/cNdEgnCmNU0 Muller-Breslau Method (the easy method!) - https://youtu.be/1VcwsaQeUMY

The Muller-Breslau Principle gives us an easy, geometric way of constructing influence lines. This video covers how to solve for an influence line using Muller-Breslau, then lays out some rules to follow that will help you always draw the right shape for determinate and indeterminate systems. Finally, the video concludes with an example of how to use geometry to find not only the shape, but also the values of influence lines using geometry.

This video defines the concept of an influence line for a moving loads across a structure. This is a very useful technique in bridge engineering. An influence line plots a specific action (for example, a reaction force or the shear or moment at a specific point) for a unit load at position x, moving along the structure. These can be used to find the extreme loading events for a specific demand. This video covers how to solve for an influence line using statics. The Muller-Breslau principle, which can be used to find influence lines using geometry, will be illustrated in a follow-up video.

This video defines projects loads and presents an example problem using the most common type of projected load, snow loading on a roof truss. In this example, we will: 1) Compute the reactions forces for combined dead plus snow loading 2) Convert projected loads to distributed loads in the axial and shear directions 3) Compute the axial, shear, and moment diagrams. For a projected load S, with an angle A between the loading plane and the element to which the load is applied, there are a few shortcut equations: ~ Distributed Shear Load = S*cos(A)*cos(A) ~ Distributed Axial Load = S*cos(A)*sin(A) Try these out, and you'll see they match exactly the results shown in the video! In this example, cos(A) = 12/13 and sin(A) = 5/13.

This video presents a detailed example problem of computing and drawing the axial, shear, and moment diagrams in structures with multiple elements coming together: in this case, frames. In this example, we will: 1) Compute the reactions forces 2) Define the coordinate systems for each column or beam 3) Draw the internal force diagrams for each element 4) Summarize the results by superposing the diagrams on the structure Special attention should always be given to the sign convention and coordinate system for each element. Designing for a compressive versus tensile axial force are very different things, and when designing for bending moment, we need to know which part of the section is in tension versus compression. Fortunately for shear, the sign convention is not as important in design, though it is important for correctly deriving the moment diagram.