The document discusses portal structures, which are commonly used in warehouse, hangar, and bridge construction. It covers symmetric and asymmetric portal structures that carry various load combinations, including centered vertical loads, horizontal loads, and distributed loads. Methods for calculating the reactions, shear forces, bending moments, and normal stresses in the structural elements are presented. Free body diagrams are used to illustrate the distribution of internal forces.
Modul 4-balok menganjur diatas dua perletakanMOSES HADUN
This module discusses overhanging beams supported above two supports. It covers beams carrying concentrated, uniformly distributed, and combined loads on one or both sides of the supports. The learning objectives are for students to understand internal forces (moments and shears) in overhanging beams and be able to calculate and illustrate them. The materials will be beams with one-sided loading carrying concentrated, uniformly distributed, or combined loads, and beams with loading on both sides carrying concentrated or uniformly distributed loads. Example calculations of reactions, shearing forces, and bending moments are provided.
The document discusses portal structures, which are commonly used in warehouse, hangar, and bridge construction. It covers symmetric and asymmetric portal structures that carry various load combinations, including centered vertical loads, horizontal loads, and distributed loads. Methods for calculating the reactions, shear forces, bending moments, and normal stresses in the structural elements are presented. Free body diagrams are used to illustrate the distribution of internal forces.
Dokumen ini memberikan penjelasan tentang cara menggambar garis pengaruh reaksi dan gaya batang pada struktur rangka baja. Dijelaskan bahwa garis pengaruh reaksi bergantung pada posisi beban dan nilainya berubah secara linier tergantung panjang batang. Metode Ritter digunakan untuk menentukan besar gaya batang dengan asumsi beban tunggal pada posisi tertentu. Gambar gaya batang dihasilkan untuk contoh struktur yang d
Modul 7-bangunan portal , statika dan mekanika dasar MOSES HADUN
The document discusses portal structures, which are commonly used in warehouse, hangar, and bridge construction. It covers symmetric and asymmetric portal structures that carry various load combinations, including centered vertical loads, horizontal loads, and distributed loads. Methods for calculating the reactions, shear forces, bending moments, and normal stresses in the structural elements are presented. Free body diagrams are used to illustrate the distribution of internal forces.
The document discusses portal structures, which are commonly used in warehouse, hangar, and bridge construction. It covers symmetric and asymmetric portal structures that carry various load combinations, including centered vertical loads, horizontal loads, and distributed loads. Methods for calculating the reactions, shear forces, bending moments, and normal stresses in the structural elements are presented. Free body diagrams are used to illustrate the distribution of internal forces.
Modul 4-balok menganjur diatas dua perletakanMOSES HADUN
This module discusses overhanging beams supported above two supports. It covers beams carrying concentrated, uniformly distributed, and combined loads on one or both sides of the supports. The learning objectives are for students to understand internal forces (moments and shears) in overhanging beams and be able to calculate and illustrate them. The materials will be beams with one-sided loading carrying concentrated, uniformly distributed, or combined loads, and beams with loading on both sides carrying concentrated or uniformly distributed loads. Example calculations of reactions, shearing forces, and bending moments are provided.
The document discusses portal structures, which are commonly used in warehouse, hangar, and bridge construction. It covers symmetric and asymmetric portal structures that carry various load combinations, including centered vertical loads, horizontal loads, and distributed loads. Methods for calculating the reactions, shear forces, bending moments, and normal stresses in the structural elements are presented. Free body diagrams are used to illustrate the distribution of internal forces.
Dokumen ini memberikan penjelasan tentang cara menggambar garis pengaruh reaksi dan gaya batang pada struktur rangka baja. Dijelaskan bahwa garis pengaruh reaksi bergantung pada posisi beban dan nilainya berubah secara linier tergantung panjang batang. Metode Ritter digunakan untuk menentukan besar gaya batang dengan asumsi beban tunggal pada posisi tertentu. Gambar gaya batang dihasilkan untuk contoh struktur yang d
Modul 7-bangunan portal , statika dan mekanika dasar MOSES HADUN
The document discusses portal structures, which are commonly used in warehouse, hangar, and bridge construction. It covers symmetric and asymmetric portal structures that carry various load combinations, including centered vertical loads, horizontal loads, and distributed loads. Methods for calculating the reactions, shear forces, bending moments, and normal stresses in the structural elements are presented. Free body diagrams are used to illustrate the distribution of internal forces.
Balok Gerber adalah balok yang ditopang oleh dua tumpuan atau lebih. Perhitungannya menggunakan statika tak tentu dengan memasukkan sendi antara tumpuan. Jumlah sendi ditentukan oleh rumus jumlah sendi = jumlah tumpuan - 2. Dokumen ini memberikan contoh soal perhitungan reaksi dan momen pada balok Gerber dengan berbagai variasi jumlah tumpuan dan beban.
Modul kuliah membahas pelengkung tiga sendi dan cara penyelesaiannya. Struktur pelengkung tiga sendi dapat memikul beban titik tunggal atau kombinasi beban titik vertikal dan horizontal. Langkah penyelesaiannya meliputi menghapus sendi tengah dan mengganti tumpuan dengan rol, menentukan reaksi tumpuan, lalu mengembalikan struktur semula untuk menentukan gaya pelengkung.
The document discusses different types of portals and arches. It provides examples of simple portals, 3-hinge portals, simple arches, and 3-hinge arches. It analyzes the reactions, shear forces, bending moments, and normal forces of each structure. Example problems are also given to demonstrate calculating the forces in different portal frames with point or uniformly distributed loads.
1) This document analyzes the forces and moments in an asymmetrical three-hinged portal frame with two different configurations.
2) For the first configuration, the vertical and horizontal reactions are calculated. The internal forces are then determined, including axial forces, shear forces, and bending moments.
3) The second configuration is similarly analyzed, with the vertical and horizontal reactions calculated first, followed by the internal forces.
Dokumen tersebut membahas tentang struktur statis tertentu pada mekanika struktur, dimana struktur tersebut dapat diselesaikan menggunakan persamaan keseimbangan berupa jumlah gaya horizontal, vertikal dan momen yang sama dengan nol. Contoh struktur statis tertentu adalah balok diatas dua perletakan dengan jumlah reaksi yang tidak diketahui maksimal tiga. Dokumen juga menjelaskan tentang gaya-gaya dalam sepert
MEKANIKA REKAYASA 3 (METODE DALIL 3 MOMEN DAN METODE CROSS)Sumarno Feriyal
This document describes the analysis of a beam-column structure subjected to loads. The structure consists of five sections A-B, B-C, C-D, D-E connected by joints. Three methods are used to solve for the internal forces: (1) moment area method, (2) three-moment equation method, and (3) cross-section method. The moment area method is used to calculate the internal moments, then the three-moment equation and cross-section methods are used to solve for the internal forces at each joint. Finally, the support reactions are calculated by considering equilibrium at each support.
1. The document analyzes the structure of a plane frame using the slope deflection method. It presents the problem of a portal frame under loading and goes through the steps of the slope deflection method.
2. The steps include determining degrees of freedom, member forces, member stiffness, developing the slope deflection equations, solving for unknown slopes, calculating member moments, drawing free body diagrams, and constructing shear and moment diagrams.
3. Diagrams are presented for the shear, moment and axial force (N) diagrams, showing the distribution of these effects along each member of the frame.
1. Dokumen ini membahas tentang definisi pantai, angin, fetch, gelombang, dan karakteristik gelombang seperti deformasi meliputi refraksi, difraksi, refleksi, dan gelombang pecah.
Garis pengaruh digunakan untuk menggambarkan pengaruh beban bergerak terhadap reaksi perletakan, gaya lintang, dan momen. Dengan menghitung nilai-nilai tersebut pada beberapa posisi beban dan menghubungkannya, didapatkan garis pengaruh yang menunjukkan pengaruh maksimal beban terhadap struktur.
Dokumen tersebut membahas tentang tekanan tanah dalam keadaan diam, tekanan tanah aktif dan pasif menurut Rankine, serta diagram dan distribusi tekanan tanah ke samping yang bekerja pada tembok penahan. Topik utama mencakup konsep tekanan tanah dalam konstruksi penahan tanah seperti dinding penahan dan distribusi tekanannya pada berbagai kondisi tanah dan permukaan.
Dokumen tersebut membahas perencanaan geometrik jalan yang meliputi peta kontur, rencana trase jalan, penentuan medan jalan, perhitungan alinyemen horizontal dan vertikal, serta perhitungan jarak pandang. Dokumen ini memberikan panduan dasar untuk merencanakan geometri jalan seperti menentukan jenis dan bentuk tikungan berdasarkan kecepatan rencana jalan.
Modul ini membahas tentang muatan tidak langsung pada struktur, termasuk beban tidak langsung, sendi gerber, dan contoh soal perhitungan muatan terbagi rata dan terpusat. Tujuan pembelajaran adalah memahami gaya-gaya dalam struktur akibat muatan tidak langsung dan konstruksi gelagar dengan sendi gerber.
Modul 4-balok menganjur diatas dua perletakanMOSES HADUN
The document discusses beam structures that project over two supports (overhangs) and are loaded in various ways. It provides 5 examples of overhang beams with different load configurations: 1) a centered point load, 2) a uniformly distributed load, 3) a combination of uniform and point loads, 4) centered point loads on both sides, and 5) a uniform load on both sides. For each example, it solves for the support reactions, internal shear forces, and bending moments. The goal is for students to understand the internal forces in overhang beams under different loading conditions and be able to calculate the reactions, shear forces, and bending moments.
The document discusses beams supported on two supports. It contains 5 topics:
1) A beam carrying a concentrated central load.
2) A beam carrying eccentric central loads.
3) A beam carrying a uniformly distributed load.
4) A beam carrying a triangular load.
5) A beam carrying a combination of loads.
The purpose is for students to understand internal forces (bending moment and shear force) in beams supported on two supports under different load conditions and to calculate and illustrate them. Detailed calculations are shown for each load condition.
Balok Gerber adalah balok yang ditopang oleh dua tumpuan atau lebih. Perhitungannya menggunakan statika tak tentu dengan memasukkan sendi antara tumpuan. Jumlah sendi ditentukan oleh rumus jumlah sendi = jumlah tumpuan - 2. Dokumen ini memberikan contoh soal perhitungan reaksi dan momen pada balok Gerber dengan berbagai variasi jumlah tumpuan dan beban.
Modul kuliah membahas pelengkung tiga sendi dan cara penyelesaiannya. Struktur pelengkung tiga sendi dapat memikul beban titik tunggal atau kombinasi beban titik vertikal dan horizontal. Langkah penyelesaiannya meliputi menghapus sendi tengah dan mengganti tumpuan dengan rol, menentukan reaksi tumpuan, lalu mengembalikan struktur semula untuk menentukan gaya pelengkung.
The document discusses different types of portals and arches. It provides examples of simple portals, 3-hinge portals, simple arches, and 3-hinge arches. It analyzes the reactions, shear forces, bending moments, and normal forces of each structure. Example problems are also given to demonstrate calculating the forces in different portal frames with point or uniformly distributed loads.
1) This document analyzes the forces and moments in an asymmetrical three-hinged portal frame with two different configurations.
2) For the first configuration, the vertical and horizontal reactions are calculated. The internal forces are then determined, including axial forces, shear forces, and bending moments.
3) The second configuration is similarly analyzed, with the vertical and horizontal reactions calculated first, followed by the internal forces.
Dokumen tersebut membahas tentang struktur statis tertentu pada mekanika struktur, dimana struktur tersebut dapat diselesaikan menggunakan persamaan keseimbangan berupa jumlah gaya horizontal, vertikal dan momen yang sama dengan nol. Contoh struktur statis tertentu adalah balok diatas dua perletakan dengan jumlah reaksi yang tidak diketahui maksimal tiga. Dokumen juga menjelaskan tentang gaya-gaya dalam sepert
MEKANIKA REKAYASA 3 (METODE DALIL 3 MOMEN DAN METODE CROSS)Sumarno Feriyal
This document describes the analysis of a beam-column structure subjected to loads. The structure consists of five sections A-B, B-C, C-D, D-E connected by joints. Three methods are used to solve for the internal forces: (1) moment area method, (2) three-moment equation method, and (3) cross-section method. The moment area method is used to calculate the internal moments, then the three-moment equation and cross-section methods are used to solve for the internal forces at each joint. Finally, the support reactions are calculated by considering equilibrium at each support.
1. The document analyzes the structure of a plane frame using the slope deflection method. It presents the problem of a portal frame under loading and goes through the steps of the slope deflection method.
2. The steps include determining degrees of freedom, member forces, member stiffness, developing the slope deflection equations, solving for unknown slopes, calculating member moments, drawing free body diagrams, and constructing shear and moment diagrams.
3. Diagrams are presented for the shear, moment and axial force (N) diagrams, showing the distribution of these effects along each member of the frame.
1. Dokumen ini membahas tentang definisi pantai, angin, fetch, gelombang, dan karakteristik gelombang seperti deformasi meliputi refraksi, difraksi, refleksi, dan gelombang pecah.
Garis pengaruh digunakan untuk menggambarkan pengaruh beban bergerak terhadap reaksi perletakan, gaya lintang, dan momen. Dengan menghitung nilai-nilai tersebut pada beberapa posisi beban dan menghubungkannya, didapatkan garis pengaruh yang menunjukkan pengaruh maksimal beban terhadap struktur.
Dokumen tersebut membahas tentang tekanan tanah dalam keadaan diam, tekanan tanah aktif dan pasif menurut Rankine, serta diagram dan distribusi tekanan tanah ke samping yang bekerja pada tembok penahan. Topik utama mencakup konsep tekanan tanah dalam konstruksi penahan tanah seperti dinding penahan dan distribusi tekanannya pada berbagai kondisi tanah dan permukaan.
Dokumen tersebut membahas perencanaan geometrik jalan yang meliputi peta kontur, rencana trase jalan, penentuan medan jalan, perhitungan alinyemen horizontal dan vertikal, serta perhitungan jarak pandang. Dokumen ini memberikan panduan dasar untuk merencanakan geometri jalan seperti menentukan jenis dan bentuk tikungan berdasarkan kecepatan rencana jalan.
Modul ini membahas tentang muatan tidak langsung pada struktur, termasuk beban tidak langsung, sendi gerber, dan contoh soal perhitungan muatan terbagi rata dan terpusat. Tujuan pembelajaran adalah memahami gaya-gaya dalam struktur akibat muatan tidak langsung dan konstruksi gelagar dengan sendi gerber.
Modul 4-balok menganjur diatas dua perletakanMOSES HADUN
The document discusses beam structures that project over two supports (overhangs) and are loaded in various ways. It provides 5 examples of overhang beams with different load configurations: 1) a centered point load, 2) a uniformly distributed load, 3) a combination of uniform and point loads, 4) centered point loads on both sides, and 5) a uniform load on both sides. For each example, it solves for the support reactions, internal shear forces, and bending moments. The goal is for students to understand the internal forces in overhang beams under different loading conditions and be able to calculate the reactions, shear forces, and bending moments.
The document discusses beams supported on two supports. It contains 5 topics:
1) A beam carrying a concentrated central load.
2) A beam carrying eccentric central loads.
3) A beam carrying a uniformly distributed load.
4) A beam carrying a triangular load.
5) A beam carrying a combination of loads.
The purpose is for students to understand internal forces (bending moment and shear force) in beams supported on two supports under different load conditions and to calculate and illustrate them. Detailed calculations are shown for each load condition.
Newton's method and Gauss-Newton method can be used to minimize a nonlinear least squares function to fit a vector of model parameters to a data vector. The Gauss-Newton method approximates the Hessian matrix as the Jacobian transpose times the Jacobian, ignoring additional terms, making it faster to compute but less accurate than Newton's method. The Levenberg-Marquardt method interpolates between Gauss-Newton and steepest descent methods to provide a balance of convergence speed and accuracy. Iterative methods like conjugate gradients are useful for large nonlinear problems where storing and inverting the full matrix would be prohibitive. L1 regression provides a more robust alternative to L2 regression for dealing with outliers through minimization of the absolute error rather
This document describes a damped oscillation graph of a spring-mass system experiencing dry frictional force. The system performs damped harmonic oscillation as the mass oscillates back and forth along the horizontal surface. The document provides the equation of motion, solution, and a Maple code to plot the decreasing amplitude oscillation graph over multiple periods as a function of time.
1. The document discusses Laplace transforms and provides definitions, properties, and examples. Laplace transforms take a function of time and transform it into a function of a complex variable s.
2. Key properties discussed include linearity, shifting theorems, and Laplace transforms of common functions like 1, t, e^at, sin(at), etc. Explicit formulas for the Laplace transforms of these functions are given.
3. Examples of calculating Laplace transforms of various functions are provided.
This document summarizes solutions to three theoretical questions:
1) Describes how to use measurements of gravitational redshift to determine the mass and radius of a star.
2) Explains Snell's law and how it can be used to determine the path of light rays through a medium with a linear change in refractive index.
3) Analyzes the motion of a floating cylindrical buoy, determining equations for its vertical and rotational oscillations and relating the periods.
1) The document provides formulas and concepts from physics including kinematics, forces, circular motion, momentum, energy, springs, fluids, electricity, sound, optics, and thermodynamics.
2) Key formulas are presented for translational motion, frictional forces, circular motion, momentum, work, energy, springs, continuity of fluids, current and resistance, resistors, sound, and torque forces.
3) Memorization tips are given for pairing related concepts like force and electric force, gravitational force and coulomb force, as well as average quantities, kinetic and potential energy, pressure, specific gravity, and root mean square values.
Quantitative norm convergence of some ergodic averagesVjekoslavKovac1
The document summarizes quantitative estimates for the convergence of multiple ergodic averages of commuting transformations. Specifically, it presents a theorem that provides an explicit bound on the number of jumps in the Lp norm for double averages over commuting Aω actions on a probability space. The proof transfers the structure of the Cantor group AZ to R+ and establishes norm estimates for bilinear averages of functions on R2+. This allows bounding the variation of the double averages and proving the theorem.
The document discusses motion under central forces. It shows that the equations of motion for a two-body central force problem can be reduced to a one-body problem. For planetary motion with gravitational force, the integrals of motion lead to Kepler's laws, with orbits taking the form of ellipses, parabolas or hyperbolas depending on the value of the eccentricity parameter ε. An eccentricity of 0 gives a circular orbit, 1 gives a parabolic orbit, and above 1 gives a hyperbolic orbit.
On maximal and variational Fourier restrictionVjekoslavKovac1
Workshop talk slides, Follow-up workshop to trimester program "Harmonic Analysis and Partial Differential Equations", Hausdorff Institute, Bonn, May 2019.
This document defines and provides examples of parameterized curves in R3. It introduces the concept of a smooth curve as a smooth map from an interval to R3. Regular curves are defined as smooth curves with everywhere nonzero velocity. Examples of regular curves include circles and helices parameterized by t. Reparameterizations are introduced as changing the parameterization of a curve while tracing the same path. The length of a curve is defined using an integral of speed over the parameter. Arc length parameterization reparameterizes a curve so that the parameter is equal to arc length measured from a fixed point.
The document provides an introduction to Laplace transforms. Key points:
- Laplace transforms are a mathematical tool that converts differential equations in the time domain to algebraic equations in the complex frequency (s) domain, making problems easier to solve.
- Common transforms include impulse, step, ramp, and exponential functions.
- Properties and theorems allow transforming derivatives, integrals, shifts, and scaling.
- Tables provide standard transforms to convert between time and s domains.
- Solving problems involves taking the Laplace transform of equations, using properties to solve for the transform in s domain, then applying the inverse transform.
- Partial fraction expansions break complex fractions into simpler forms for applying transforms.
1) The document discusses horizontal forces on pile foundations, including temporary forces from wind, earthquakes, and boat impacts, as well as permanent forces from active soil pressure and groundwater pressure.
2) It explains passive soil pressure diagrams and calculations for determining the passive soil force and its point of application on a pile.
3) Formulas are provided for calculating the allowed temporary horizontal force on a pile based on the passive soil resistance, and checking if it is less than the pile's allowed design capacity.
35 tangent and arc length in polar coordinatesmath266
The document discusses parametric representations of polar curves. It begins by explaining that a rectangular curve given by y=f(x) can be parametrized as x=t and y=f(t). It then explains that a polar curve given by r=f(θ) can be parametrized as x=f(θ)cos(θ) and y=f(θ)sin(θ). Examples are given of parametrizing the Archimedean spiral r=θ and the cardioid r=1+sin(θ). Formulas are derived for calculating the slope of the tangent line to a polar curve at a given point in terms of r and θ. Examples are worked out for finding the slope
This document provides a table of commonly used Laplace transform pairs. There are 37 entries in the table that list various functions of t and their corresponding Laplace transforms F(s). Each entry is of the form f(t) = L-1{F(s)}, which relates a function f(t) to its Laplace transform F(s). Notes are provided to explain details like hyperbolic functions, the Gamma function, and limitations of the table.
This document provides a table of commonly used Laplace transform pairs. There are 37 entries in the table that list various functions of t and their corresponding Laplace transforms F(s). Each entry is of the form f(t) = L-1{F(s)}, which relates a function of time f(t) to its Laplace transform F(s). Notes are provided to explain concepts like hyperbolic functions and the Gamma function used in some of the entries.
This document provides a table of commonly used Laplace transform pairs. There are 38 entries in total, each providing the Laplace transform of a specific function. For example, entry 1 gives the Laplace transform of a constant function f(t) as F(s)=1/s. The table also includes brief explanatory notes about properties of Laplace transforms and related functions like the Gamma function.
The document discusses shear forces and bending moments in beams. It provides examples of different types of beams and loads, and how to calculate reactions, shear forces, and bending moments. Equations are given relating loads, shear forces, and bending moments. Methods are described for constructing shear force and bending moment diagrams for beams with different load conditions like concentrated loads, uniform loads, and combinations of loads.
This document discusses Laplace transforms and their application to solving differential equations. It defines the Laplace transform, provides examples of common transform pairs, and lists several properties that allow transforms to be manipulated algebraically. The document states that Laplace transforms can convert differential equations into algebraic equations in the frequency domain, making them easier to solve. The transform method involves taking the Laplace transform of the differential equation, solving for the unknown variable, and taking the inverse Laplace transform to obtain the time domain solution.
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This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
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The smart irrigation system represents an innovative approach to optimize water usage in agricultural and landscaping practices. The integration of cutting-edge technologies, including sensors, actuators, and data analysis, empowers this system to provide accurate monitoring and control of irrigation processes by leveraging real-time environmental conditions. The main objective of a smart irrigation system is to optimize water efficiency, minimize expenses, and foster the adoption of sustainable water management methods. This paper conducts a systematic risk assessment by exploring the key components/assets and their functionalities in the smart irrigation system. The crucial role of sensors in gathering data on soil moisture, weather patterns, and plant well-being is emphasized in this system. These sensors enable intelligent decision-making in irrigation scheduling and water distribution, leading to enhanced water efficiency and sustainable water management practices. Actuators enable automated control of irrigation devices, ensuring precise and targeted water delivery to plants. Additionally, the paper addresses the potential threat and vulnerabilities associated with smart irrigation systems. It discusses limitations of the system, such as power constraints and computational capabilities, and calculates the potential security risks. The paper suggests possible risk treatment methods for effective secure system operation. In conclusion, the paper emphasizes the significant benefits of implementing smart irrigation systems, including improved water conservation, increased crop yield, and reduced environmental impact. Additionally, based on the security analysis conducted, the paper recommends the implementation of countermeasures and security approaches to address vulnerabilities and ensure the integrity and reliability of the system. By incorporating these measures, smart irrigation technology can revolutionize water management practices in agriculture, promoting sustainability, resource efficiency, and safeguarding against potential security threats.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Sinan KOZAK
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
1. STATIKA I
MODUL 8
BANGUNAN PORTAL DENGAN
RASUK GERBER
Dosen Pengasuh :
Ir. Thamrin Nasution
Materi Pembelajaran :
1. Portal Kaki Tunggal dengan Rasuk Gerber Memikul Beban Terpusat.
2. Portal Kaki Tunggal dengan Rasuk Gerber, Garis Pengaruh.
3. Portal Kaki Tidak Simetris Dengan Dua Rasuk Gerber, Memikul Beban Terbagi Rata.
4. Portal Kaki Tidak Simetris Dengan Dua Rasuk Gerber, Garis Pengaruh.
WORKSHOP/PELATIHAN
Tujuan Pembelajaran :
Mahasiswa memahami dan mengetahui tentang gaya-gaya dalam dari struktur portal kaki
tunggal dan kaki tidak simetris dengan rasuk gerber, memikul beban terpusat dan terbagi
rata, mengetahui cara menggambarkan garis pengaruh.
DAFTAR PUSTAKA
a) Soemono, Ir., “STATIKA 1”, Edisi kedua, Cetakan ke-4, Penerbit ITB, Bandung, 1985.
2. thamrinnst.wordpress.com
UCAPAN TERIMA KASIH
Penulis mengucapkan terima kasih yang sebesar-besarnya kepada
pemilik hak cipta photo-photo, buku-buku rujukan dan artikel, yang terlampir
dalam modul pembelajaran ini.
Semoga modul pembelajaran ini bermanfaat.
Wassalam
Penulis
Thamrin Nasution
thamrinnst.wordpress.com
thamrin_nst@hotmail.co.id
3. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
1
BANGUNAN PORTAL DENGAN
RASUK GERBER
1. PORTAL KAKI TUNGGAL DENGAN RASUK GERBER
MEMIKUL BEBAN TERPUSAT.
Gambar 1 : Portal kaki tunggal dengan rasuk gerber, memikul beban terpusat.
Penyelesaian :
Span (S) – (F).
a. Reaksi Perletakan.
MF = 0,
RSV . L2 - P2 . e = 0
RSV = P2 . e/L2 (ton).
P1
ba
(A)
(B)
h
L1
(C)(D) (S)
P2
c d e
f
g
P3
L2
(E)
(F)
(G)
P1
ba
(A)
(B)
h
RAV
RBV
L1
(C)(D)
P2
c
d e
f
g
P3
L2
(E)
(F)
(G)
(S)
RSV
RSV
RFV
IDEALISASI STRUKTUR
(S)
RAH
4. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
2
MS = 0,
- RFV . L2 + P2 . d = 0
RFV = P2 . d/L2 (ton).
Kontrol :
V = 0,
RSV + RFV – P2 = 0
b. Gaya lintang.
DS-G = + RSF
DG-F = + RSV – P2 (ton).
DG-F = – RFV (ton).
c. M o m e n .
MS = 0
MG = + P2 . d . e/L2
MF = 0
d. Gaya Normal.
NS-F = 0 (ton).
Span (A) – (B) – (S).
a. Reaksi Perletakan.
H = 0,
RAH - P3 = 0
RAH = P3 (ton) (ke kanan)
MB = 0,
RAV . L1 + RAH . h – P1 . b + RSV . c - P3 . g = 0
RAV = + P1 . b/L1 + P3 . g/L1 – RAH . h/L1 – RSV . c/L1 (ton).
MA = 0,
- RBV . L1 + P1 . a + RSV . (c + L1) + P3 . f = 0
RBV = + P1 . a/L1 + P3 . f/L1 + RSV . (c + L1)/L1 (ton).
Kontrol :
V = 0
RAV + RBV = P1 + RSV
b. Gaya Lintang.
DA-D = + RAH (ton).
DD-C = + RAV – P1 (ton).
DC-S = + RAV – P1 + RBV = + RSV (ton).
DC-E = + RAH (ton).
DE-B = + RAH – P3 = 0 (ton).
c. M o m e n .
MA = 0
MD = + RAV . a (t.m’).
MCD = RAV . a - P1 . b (t.m’).
MCS = - RSV . c (t.m’).
MCE = - P3 . f (t.m’)
5. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
3
MB = 0
d. Gaya Normal.
NA-C = – RAH ton (tekan).
NC-B = – RBV ton (tekan).
Gambar 2 : Bidang-bidang gaya lintang, momen dan gaya normal.
ba
(A)
(B)
h
L1
(C)
(D) (S)
c d e
f
g
L2
(E)
(F)
(G)
ba
(A)
(B)
h
L1
(C)
(D) (S)
c d e
f
g
L2
(E)
(F)
(G)
ba
(A)
(B)
h
L1
(C)(D) (S)
c d e
f
g
L2
(E)
(F)
(G)
(a) Gaya Lintang
(b) M o m e n
(c) Gaya Normal
+
–
+
+
–
–
+ +
–
–
6. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
4
2. PORTAL KAKI TUNGGAL DENGAN RASUK GERBER
GARIS PENGARUH (Influence Line).
Gambar 3 : Garis pengaruh span (S)-(F), section (G).
Diminta : Gambarkanlah garis pengaruh gaya lintang, momen dan gaya normal untuk
potongan (D), (G) dan (F).
Penyelesaian :
Span (S) - (F).
a. Garis pengaruh RS.
P = 1 t berada di (S),
RS = + P = + 1 (ton)
P = 1 t berada di (G),
MF = 0
RS = + P . e/L2 = + 1 . e/L2 (ton)
P = 1 t berada di (F),
RS = 0 (ton)
b. Garis pengaruh RF
P = 1 t berada di (S),
RF = 0 (ton)
(A)
(B)
h
L1
(C)
(D)
(S)
c
(F)
(G)
L2
ed
ba
G.p. RS
G.p. RF
+1
+1
G.p. DG
+1
-1–
+
+
d.e/L2
e/L2
d/L2
G.p. MG
- d/L2
e/L2
+
7. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
5
P = 1 t berada di (G),
MS = 0
RF = + P . d/L2 = + 1 . d/L2 (ton)
P = 1 t berada di (F),
RS = + P = + 1 (ton)
c. Garis pengaruh Gaya lintang pada titik (G).
P = 1 t berada di (S),
RS = + P = + 1 t,
DG = RS – P = 0
P = 1 t berada di (G), P belum melewati (G),
MF = 0
RS = + P . e/L2 (ton)
DG = RS – P = P.e/L2 – P = P . (L2 - d)/L2 – P . L2/L2 = – P . d/L2
DG = – d/L2 (ton)
P = 1 t berada di (G), P sudah melewati (G),
MF = 0
RS = + P . e/L2 (ton)
Dc = + RS = + P . e/L2 (ton)
P = 1 t berada di (F),
MB = 0
RS = 0 (ton)
DG = RS = 0 (ton)
d. Garis pengaruh Momen pada titik (G).
P = 1 t berada di (S),
RS = + P = + 1 (ton)
MG = (RS – P) . d = 0 (t.m’)
P = 1 t berada di (G),
MF = 0
RS = + P . e/L2 = + 1 . e/L2 (t.m’)
MG = RS . d = d . e/L2 (t.m’)
P = 1 t berada di (F),
RS = 0 (ton)
MG = 0 (t.m’)
Span (A) - (B)
a. Garis pengaruh RA.
P = 1 t berada di (A),
RA = + P = + 1 (ton)
P = 1 t berada di (C),
MB = 0
RA = 0 (ton)
P = 1 t berada di (S),
MB = 0,
RA . L1 + P . c = 0
RA = - P . c/L1 = - 1 . c/L1 (ton)
P = 1 t berada di (F),
RA = 0 (ton).
8. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
6
Gambar 4 : Garis pengaruh span (A)-(B), section (D), gaya normal kolom (B)-(C).
b. Garis pengaruh RB.
P = 1 t berada di (A),
RB = 0 (ton)
P = 1 t berada di (C),
MB = 0
RB = + P = +1 (ton).
(A)
(B)
h
L1
(C)
(D)
(S)
c
f
g
(E)
(F)
(G)
L2
ed
ba
G.p. RA
G.p. RB
+1
+1
G.p. DD
+1
-1
+
+
- c/L1
G.p. MD
- a/L1
b/L1
+
+
(c + L1)/L1
–
b/L1
a/L1
–
e/L2 . (c + L1)/L1
- c/L1
–
a.b/L1
- a . c/L1
–
G.p. NB-C
- 1
- (c + L1)/L1
- a/L1
- e/L2 . (c + L1)/L1
–
9. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
7
P = 1 t berada di (S),
MA = 0,
- RB . L1 + P . (c + L1) = 0
RB = + P . (c + L1)/L1 = + 1 . (c + L1)/L1 (ton)
P = 1 t berada di (F),
RB = 0 (ton).
c. Garis pengaruh Gaya lintang pada titik (D).
P = 1 t berada di (A),
RA = + P = + 1 t,
DD = RA – P = 0
P = 1 t berada di (D), P belum melewati (D),
MB = 0
RA = + P . b/L1(ton)
DD = RA – P = P.b/L1 – P = P . (L1 - a)/L1 – P . L1/L1 = – P . a/L1
DD = – a/L1 (ton)
P = 1 t berada di (D), P sudah melewati (D),
MB = 0
RA = + P . b/L1 (ton)
DD = + RA = + P . b/L1 (ton)
P = 1 t berada di (C),
MB = 0
RA = 0 (ton)
DD = RA = 0 (ton)
P = 1 t berada di (S),
MA = 0,
+ RA . L1 + P . c = 0
RA = - P . c/L1 = - 1 . c/L1 (ton)
DD = RA = - c/L1
P = 1 t berada di (F),
RA = 0 (ton).
DD = 0 (ton).
d. Garis pengaruh Momen pada titik (D).
P = 1 t berada di (A),
RA = + P = + 1 (ton)
MD = (RA – P) . a = 0 (t.m’)
P = 1 t berada di (D),
MB = 0
RA = + P . b/L1 = + 1 . b/L1 (t.m’)
MD = RA . a = a . b/L1 (t.m’)
P = 1 t berada di (C),
RA = 0 (ton)
MD = 0 (t.m’)
P = 1 t berada di (S),
MA = 0,
+ RA . L1 + P . c = 0
RA = - P . c/L1 = - 1 . c/L1 (ton)
MD = RA . a = - a .c/L1 (t.m’)
P = 1 t berada di (F),
RA = 0 (ton).
MD = 0 (t.m’).
e. Garis pengaruh gaya normal
kolom (B)-(C).
P = 1 t berada di (A),
RB = 0 (ton)
NB-C = - RB = 0 (ton)
P = 1 t berada di (C),
MB = 0
RB = + P = +1 (ton)
NB-C = - RB = - 1 (ton).
P = 1 t berada di (S),
MA = 0,
- RB . L1 + P . (c + L1) = 0
RB = + P . (c + L1)/L1
= + 1 . (c + L1)/L1 (ton)
NB-C = - RB
= - 1 . (c + L1)/L1 (ton)
P = 1 t berada di (F),
RB = 0 (ton).
NB-C = - RB = 0 (ton)
10. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
8
3. PORTAL KAKI TIDAK SIMETRIS DENGAN DUA RASUK GERBER
MEMIKUL BEBAN TERBAGI RATA.
Gambar 5 : Portal kaki tidak simetris dengan dua rasuk gerber.
Penyelesaian :
Span (A) – (S1).
a. Reaksi Perletakan.
MS1 = 0,
RAV . L1 - ½ . q1.L1
2
= 0
RAV = ½ q1.L1 (ton).
RS1V = RAV = ½ q1.L1 (ton).
ba
(A)
(B)
(C)
(D)
c
H1
(E) (F)
(S1)
RAV RS1V
IDEALISASI STRUKTUR
L1 L3L2
(S1 ) (S2 )
H2
(A)
RS2V RDV
(S2 ) (D)
(B)
(C)
L2
H2
H1
L3
q1 t/m’ q3 t/m’
ba c
q1 t/m’ q3 t/m’
RS1V RS2V
q2 t/m’
q2 t/m’
L1
(E) (F)
(S1) (S2 )
RBV
RCV
X
11. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
9
Kontrol :
V = 0,
RAV + RS1V = q1 . L1
b. Gaya Lintang.
DAS1 = RAV = ½ q1.L1 (ton)
DS1A = RAV – q1.L1 = – RS1 = – ½ q1.L1 (ton).
c. Momen.
MA = 0 (t.m’).
Mmaks = 1/8 q1.L1
2
(t.m’).
MS1 = 0 (t.m’).
Span (S2) – (D).
a. Reaksi Perletakan.
MD = 0,
RS2V . L3 - ½ . q3.L3
2
= 0
RS2V = ½ q3.L3 (ton).
RDV = RS2V = ½ q3.L3 (ton).
Kontrol :
V = 0,
RS2V + RDV = q3 . L3
b. Gaya Lintang.
DS2D = RS2V = ½ q3.L3 (ton)
DDS2 = RS2V – q3.L3 = – RDV = – ½ q3.L3 (ton).
c. Momen.
MS2 = 0 (t.m’).
Mmaks = 1/8 q3.L3
2
(t.m’).
MD = 0 (t.m’).
Span (B) – (C).
a. Reaksi Perletakan.
MC = 0,
RBV . L2 – RS1V . (a + b) – q2.(a + b).1/2.(a + b) + q2.(c).1/2.(c) + RS2V . (c) = 0
RBV = + RS1V.(a + b)/L2 + 1/2 q2.(a + b)2
/L2 – 1/2 q2.(c)2
/L2 – RS2V.(c)/L2 = 0
MB = 0,
– RCV . L2 – RS1V . (a – H1/tg ) + q2.(L2 + c).1/2.(L2 + c) –
q2.(a + b – L2).1/2. (a + b – L2) + RS2V . (L2 + c) = 0
RCV = – RS1V.(a – H1/tg )/L2 + ½.q2.(L2 + c)2
/L2 – ½.q2.(a + b – L2)2
/L2
+ RS2V.(L2 + c)/L2
Kontrol :
V = 0,
RBV + RCV = RS1V + q2 . (a + b + c) + RS2V
b. Gaya Lintang.
DB-E = + RBV Cos
DS1E = – RS1V (ton).
RBV
RBV Cos
RBV Sin
12. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
10
DES1 = – RS1V – q2 . a (ton).
DEF = – RS1V – q2 . a + RBV (ton).
DFE = – RS1V – q2 . (a + b) + RBV (ton).
DFS2 = – RS1V – q2 . (a + b) + RBV + RCV (ton).
DS2F = – RS1V – q2 . (a + b + c) + RBV + RCV (ton) = – RS2V (ton).
c. M o m e n .
MB = 0
MEB = + RBV . a (t.m’).
MES1 = – RS1V . a – ½.q2 . a2
(t.m’).
MEF = – RS1V . a – ½.q2 . a2
+ RBV . a (t.m’).
Momen yang terjadi pada titik sejauh x dari (F),
Mx = – RS1V . (a + x) – ½.q2 . (a + x)2
+ RBV . (H1/tan + x)
Momen maksimum terjadi pada titik dimana gaya lintang Dx = 0, yaitu
Mx = – RS1V.a – RS1V . x – ½.q2 . (a2
+ 2ax + x2
) + RBV . (H1/tan + x)
d(Mx)/dx = – RS1V – q2 . a – q2 . x + RBV = 0
x = (– RS1V – q2 . a + RBV)/q2 (m), dari titik (E).
Titik dimana momen Mx = 0, adalah
Mx = – RS1V . (a + x) – ½.q2 . (a + x)2
+ RBV . (H1/tan + x) = 0
½.q2 . (a + x)2
+ RS1V . (a + x) – RBV . (H1/tan + x) = 0
Selanjutnya persamaan diatas diselesaikan dengan rumus abc, sebagai berikut,
a
acbb
x
2
42
2,1
MFE = – RS1V . a – ½.q2.(a + b)2
+ RBV . a (t.m’).
Atau,
MFS2 = – RS2V . c – ½.q2 . c 2
(t.m’).
MFE = MFS2 (t.m’).
MFC = 0 (t.m’).
d. Gaya Normal.
NB-E = – RBV Sin (ton) (tekan).
NC-F = – RCV (ton) (tekan).
13. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
11
Gambar 6 : Bidang-bidang gaya lintang, momen dan gaya normal..
(A)
(B)
(C)
(D)
(E)
(F)
L1 L3
(S1 )
(S2 )
+
+ +
+
–– –
L2
(A)
(B)
(C)
(D)
(E)
(F)
L1 L3
(S1 ) (S2 )
+
+
––
L2
+ +(F)
(A)
(B)
(C)
(D)
(E)
L1 L3
(S1 ) (S2 )
L2
(F)
––
Bidang
Gaya Lintang
Bidang
M o m e n
Bidang
Gaya Normal
ba c
H1
H2
RBV RBV Sin
RBV Cos
14. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
12
4. PORTAL KAKI TIDAK SIMETRIS DENGAN DUA RASUK GERBER
GARIS PENGARUH.
Gambar 7 : Garis pengaruh reaksi, gaya lintang dan momen balok A-S1, S2-D dan balok E-F .
(A)
(B)
(C)
(D)
(E) (F)
L1 L3
(S1 ) (S2 )
+
L2
(F)
G.P.RA
G.P.RS1
+1
+1
+1
-1
G.P.D
G.P.M
+
+
+
+
G.P.RD
G.P.RS2
+1
+1
+1
-1
G.P.D
G.P.M
+
+
+
––
+1
ba c
G.P.RB
–
+
- c/L2
+ (a + b)/L2
+1
G.P.RC
–
+
+ (L2 + c)/L2
- (a – H1/tan )/L2
+
X
(a – H1/tan )/L2
- c/L2
+1
- 1
x
G.P.DX
G.P.MX
–
–
–
15. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
13
Gambar 8 : Garis pengaruh gaya normal dan gaya lintang kolom B – E dan C – F.
(A)
(B)
(C)
(D)
(E) (F)
L1 L3
(S1 ) (S2 )
L2
(F)
- 1 . Sin
ba c
G.P.NB-E
–
c/L2 Sin
- (a + b)/L2 . Sin
- 1
G.P.NC-F
–
- (L2 + c)/L2
(a – H1/tan )/L2
+
x
1 . Cos
G.P.DB-E
–
c/L2 Sin
(a + b)/L2 . Cos
+
+
Garis pengaruh Gaya Normal dan Gaya lintang kolom B – E
Garis pengaruh Gaya Normal kolom C – F
RBV RBV Sin
RBV Cos
16. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
14
WORKSHOP/PELATIHAN
Diketahui : Struktur seperti tergambar.
Diminta : Gambarkan bidang-bidang gaya lintang, momen dan gaya normal pada
seluruh bentang.
Penyelesaian :
DATA.
No. L1 L2 a h b c q P
Stb. m m m m m m t/m' ton
-1 4.00 2.50 1.00 4.00 1.60 2.40 1.00 2.00
0 4.40 2.70 1.10 4.10 1.64 2.46 1.25 2.15
1 4.80 2.90 1.20 4.20 1.68 2.52 1.50 2.30
2 5.20 3.10 1.30 4.30 1.72 2.58 1.75 2.45
3 5.60 3.30 1.40 4.40 1.76 2.64 2.00 2.60
4 6.00 3.50 1.50 4.50 1.80 2.70 2.25 2.75
5 6.40 3.70 1.60 4.60 1.84 2.76 2.50 2.90
6 6.80 3.90 1.70 4.70 1.88 2.82 2.75 3.05
7 7.20 4.10 1.80 4.80 1.92 2.88 3.00 3.20
8 7.60 4.30 1.90 4.90 1.96 2.94 3.25 3.35
9 8.00 4.50 2.00 5.00 2.00 3.00 3.50 3.50
(A)
(B)
h
L1
(C)
(D) (S)
a
b
c
P
L2
(E)
q t/m’
(A)
(B)
h
L1
(D) (S)
a
b
c
P
L2
(E)
q t/m’
RAV
RAH
RBV
RSV
RSV
RCV
q t/m’
IDEALISASI STRUKTUR
X
17. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
15
Pada contoh ini, X = -1
SPAN (S) – (C)
a). Reaksi perletakan.
RSV = ½ q L2 = ½ . (1 t/m’) . (2,50 m) = 1,25 ton.
RCV = RSV = ½ q L2 = 1,25 ton.
Kontrol :
RSV + RCV = q . L2
1,25 ton + 1,25 ton = (1 t/m’).(2,5 m) (memenuhi).
b). Gaya lintang.
DSC = + RSV = + 1,25 ton.
DCS = + RSV – q.L2 = 1,25 ton – (1 t/m’).(2.5 m) = – 1,25 ton.
c). Momen.
Mmaks = 1/8 q.L2
2
= 1/8 . (1 t/m’).(2,5 m)2
= 0,78125 t.m’.
SPAN (A) – (B) – (S)
a). Reaksi perletakan.
H = 0,
RAH + P = 0
RAH = – P = – 2,000 ton (ke kiri).
MB = 0,
RAV . L1 – RAH . h – ½ . q . L1
2
+ ½ . q . a2
+ RSV . a + P . c = 0
RAV = RAH . h/L1 + ½ . q . (L1
2
– a2
)/L1 – RSV . a/L1 – P . c/L1
= (2,0 t).(4,0 m)/(4,0 m) + ½.(1 t/m’).{(4 m)2
– (1 m)2
}/(4 m) – (1,25 t).(1 m)/(4 m)
– (2 t).(2,40 m)/(4 m)
RAV = 2,0000 + 1,8750 – 0,3125 – 1,2000 = 2,3625 ton.
MA = 0,
– RBV . L1 + ½ . q . (L1 + a)2
+ RSV . (L1 + a) – P . b = 0
RBV = ½ . q . (L1 + a)2
/L1 + RSV . (L1 + a)/L1 – P . b/L1
= ½.(1 t/m’).{(4 m) + (1 m)}2
/(4 m) + (1,25 t).{(4 m) + (1 m)}/(4 m)
– (2 t).(1,6 m)/(4 m)
RBV = 3,1250 + 1,5625 – 0,8000 = 3,8875 ton.
Kontrol :
RAV + RBV = q . (L1 + a) + RSV
0,3625 t + 3,8875 t = (1 t/m’) . (4 m + 1 m) + 1,250 t
6,250 t = 6,250 t (memenuhi)
b. Gaya Lintang.
DAD = + RAV = + 2,3625 (ton).
DDA = + RAV – q . L1 = 2,3625 – (1 t/m’).(4 m) = – 1,6375 (ton).
DDS = + RAV – q . L1 + RBV = 2,3625 – (1 t/m’).(4 m) + 3,8875 = + 2,250 (ton).
Atau,
DDS = + q . a + RSV = (1 t/m’).(1 m) + 1,25 = + 2,250 (ton)
DDE = – RAH = – 2 (ton).
DEB = – RAH + P = – 2 + 2 = 0 (ton).
c. M o m e n .
MA = 0
MDA = + RAV . L1 – ½ . q . L1
2
= (2,3625 t).(4 m) – ½.(1 t/m’).(4 m)2
= + 1,4500 (t.m’).
MDS = – ½ . q . a2
– RSV . a = – ½.(1 t/m’).(1 m)2
– (1,25 t).(1 m) = – 1,7500 (t.m’).
MDE = + P . b = + (2 t) . (1,6 m) = + 3,2000 (t.m’).
18. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
16
Momen yang terjadi pada titik X sejauh x dari (A),
Mx = + RAV . x – ½.q . x2
Momen maksimum terjadi pada titik dimana gaya lintang Dx = 0, yaitu
d(Mx)/dx = RAV – q . x = 0
x = RAV/q = (2,3625 t)/(1 t/m’) = 2,3625 (m), dari titik (A).
Mmaks = (2,3625 t).(2,3625 m) – ½ . (1 t/m’) . (2,3625 m)2
= 2,79070 (t.m’).
Apabila pada bentang (A)-(D), momen MDA bertanda positip, maka tidak terdapat titik
peralihan momen dari positip ke negatip, titik dimana momen Mx = 0.
Apabila MDA bertanda negatip, maka
Mx = + RAV . x – ½.q . x2
= 0
RAV – ½.q . x = 0
x = 2 RAV/q
d. Gaya Normal.
NA-D = + RAH = + 2,000 (ton) (tarik).
NB-D = – RBV = – 3,8875 (ton) (tekan).
e. Bidang-bidang gaya lintang, momen dan gaya normal dipersilahkan digambar sendiri.
Kunci Jawaban
SPAN (S) – (C)
No. RSV RCV DSC DSC Mmaks
Stb. ton ton ton ton t.m'
-1 1.250 1.250 1.250 -1.250 0.78125
0 1.688 1.688 1.688 -1.688 1.13906
1 2.175 2.175 2.175 -2.175 1.57688
2 2.713 2.713 2.713 -2.713 2.10219
3 3.300 3.300 3.300 -3.300 2.72250
4 3.938 3.938 3.938 -3.938 3.44531
5 4.625 4.625 4.625 -4.625 4.27813
6 5.363 5.363 5.363 -5.363 5.22844
7 6.150 6.150 6.150 -6.150 6.30375
8 6.988 6.988 6.988 -6.988 7.51156
9 7.875 7.875 7.875 -7.875 8.85938
SPAN (A) – (B) – (S)
Reaksi Perletakan
No. RAH RAV RBV RAV + RBV q.(L1+a)+RSV
Stb. ton ton ton ton ton
-1 2.0000 2.3625 3.8875 6.250 6.250
0 2.1500 2.9576 5.6049 8.563 8.563
1 2.3000 3.6363 7.5388 11.175 11.175
2 2.4500 4.3979 9.6896 14.088 14.088
3 2.6000 5.2421 12.0579 17.300 17.300
4 2.7500 6.1688 14.6438 20.813 20.813
5 2.9000 7.1775 17.4475 24.625 24.625
6 3.0500 8.2682 20.4693 28.738 28.738
7 3.2000 9.4408 23.7092 33.150 33.150
8 3.3500 10.6952 27.1673 37.863 37.863
9 3.5000 12.0313 30.8438 42.875 42.875
19. Modul kuliah “STATIKA 1” , Modul 8, 2012 Ir. Thamrin Nasution
Departemen Teknik Sipil, FTSP. ITM.
17
Gaya Lintang
No. DAD DDA DDS kiri DDS kanan DDE DEB
Stb. ton ton ton ton ton ton
-1 2.3625 -1.6375 2.2500 2.2500 -2.000 0.0
0 2.9576 -2.5424 3.0625 3.0625 -2.150 0.0
1 3.6363 -3.5638 3.9750 3.9750 -2.300 0.0
2 4.3979 -4.7021 4.9875 4.9875 -2.450 0.0
3 5.2421 -5.9579 6.1000 6.1000 -2.600 0.0
4 6.1688 -7.3313 7.3125 7.3125 -2.750 0.0
5 7.1775 -8.8225 8.6250 8.6250 -2.900 0.0
6 8.2682 -10.4318 10.0375 10.0375 -3.050 0.0
7 9.4408 -12.1592 11.5500 11.5500 -3.200 0.0
8 10.6952 -14.0048 13.1625 13.1625 -3.350 0.0
9 12.0313 -15.9688 14.8750 14.8750 -3.500 0.0
M o m e n
No. MDA MDS MDE x = RAV/q Mmaks x = 2RAV/q
Stb. t.m' t.m' t.m' m t.m' m
-1 1.45000 -1.75000 3.20000 2.36250 2.79070 -
0 0.91350 -2.61250 3.52600 2.36609 3.49899 -
1 0.17400 -3.69000 3.86400 2.42417 4.40744 -
2 -0.79100 -5.00500 4.21400 2.51308 5.52611 5.026
3 -2.00400 -6.58000 4.57600 2.62107 6.87002 5.242
4 -3.48750 -8.43750 4.95000 2.74167 8.45633 5.483
5 -5.26400 -10.60000 5.33600 2.87100 10.30330 5.742
6 -7.35600 -13.09000 5.73400 3.00663 12.42977 6.013
7 -9.78600 -15.93000 6.14400 3.14694 14.85489 6.294
8 -12.57650 -19.14250 6.56600 3.29083 17.59804 6.582
9 -15.75000 -22.75000 7.00000 3.43750 20.67871 6.875
Gaya Normal
No. NA-D NB-D
Stb. ton ton
-1 2.0000 -3.8875
0 2.1500 -5.6049
1 2.3000 -7.5388
2 2.4500 -9.6896
3 2.6000 -12.0579
4 2.7500 -14.6438
5 2.9000 -17.4475
6 3.0500 -20.4693
7 3.2000 -23.7092
8 3.3500 -27.1673
9 3.5000 -30.8438