When solving a statics problem with a fixed support (cantilever beam or a beam with one fixed end and other supports), follow these 7 steps:

Crucial tip for fixed supports: Always take the sum of moments about the fixed point – then (R_x) and (R_y) have zero moment arm, so (M_A) is directly determined.

Author: [Generated for educational purposes]
Subject: Physics / Technical Mechanics – Statics
Grade Level: 3rd or 4th year of secondary school (Gymnasium or Technical School)
Length: Approx. 2500+ words

Task 1:
(R_Ay = 1200 + 800 = 2000\ \textN upward)
(M_A = 1200\cdot 1 + 800\cdot 2.5 = 1200 + 2000 = 3200\ \textNm CCW)
(R_Ax=0)

Task 2:
Resolve: Horizontal 300 N at 1.5 m above A → creates moment.
(R_Ax + 300 = 0 \Rightarrow R_Ax = -300\ \textN) (left)
(R_Ay - 500 = 0 \Rightarrow R_Ay = 500\ \textN up)
(M_A + (300\cdot 1.5) - (500\cdot 3) = 0 \Rightarrow M_A + 450 - 1500 = 0 \Rightarrow M_A = 1050\ \textNm CCW)

Task 3:
(F_eq = 1200\ \textN) at 4 m from A (2/3 from free end = 4 m from fixed end)
(R_Ay = 1200\ \textN up)
(M_A = 1200 \cdot 4 = 4800\ \textNm CCW)

Task 4 (indeterminate – sample symmetric solution):
Assume symmetry only if load is centered – here it is not. In high school, sometimes they assume both ends provide equal moments and forces to satisfy statics, but correct solution requires deformation. Discuss with teacher.

Task 5:
Unknowns: fixed A gives 3, roller B gives 1 → total 4 unknowns. Only 3 equations → statically indeterminate. Additional info: e.g., beam’s flexural rigidity or a measured deflection at B.

End of Paper

This paper is intended for educational purposes and follows the standard high school statics curriculum in Serbia, Croatia, Bosnia and Herzegovina, and Montenegro.

Statika (static) tasks for secondary schools typically focus on structural balance—ensuring that a body remains at rest under various forces. The most common problems involve determining support reactions for beams (nosači) using the three basic equilibrium equations: Core Concepts in Secondary School Statics

Secondary school statics, often taught within the subject "Tehnička mehanika," generally covers:

Types of Supports: Fixed (nepokretni) and movable (pokretni) supports, and their corresponding reaction forces.

Equilibrium of a Material Point: Analyzing concurrent force systems using graphical or analytical methods.

Equilibrium of a Rigid Body: Calculating moments and forces on beams, consoles (konzole), and frames.

Friction (Trenje): Problems involving sliding friction on horizontal or inclined planes. Educational Resources & Problem Sets

You can find comprehensive reports and PDF collections of solved problems on the following platforms: Scribd Collections: Numerous digital booklets such as Zbirka rešenih zadataka iz statike and Statika: Riješeni zadaci i primjeri offer step-by-step solutions for beams and trusses.

Academic Repositories: Platforms like Palata Znanja and university sites such as Srboljub Simić's Exercises provide specialized exercise sheets covering everything from basic forces to complex truss systems (rešetkasti nosači).

Video Tutorials: For visual learners, channels like Tanja Kalman Šipoš provide detailed walkthroughs for Riter's method and finding center of gravity. Example Task Structure: Beam Reactions

Define the System: Identify the beam length, applied forces (concentrated or continuous), and moments.

Free Body Diagram (FBD): Replace supports with reaction forces ( Axcap A sub x Aycap A sub y for fixed; Bycap B sub y for movable). Equilibrium Equations:

Verification: Check the results using a moment equation at a different point (e.g., Zbirka Resenih Zadataka Iz Statike PDF - Scribd

Ovaj članak pruža pregled ključnih koncepata i rešenih primera iz oblasti statike za srednju školu, sa fokusom na fiksne oslonce (nepokretne zglobne oslonce i uklještenja) koji su temelj tehničke mehanike. Šta su fiksni oslonci u statici?

U statici, oslonci su veze koje ograničavaju kretanje tela. Kada govorimo o "fixed" ili fiksnim (nepomičnim) vezama, najčešće mislimo na dva tipa:

Nepokretni zglobni oslonac: Sprečava pomeranje tačke u bilo kom pravcu u ravni, ali dozvoljava rotaciju oko te tačke. Reakcija se sastoji od dve komponente: horizontalne ( FAxcap F sub cap A x end-sub ) i vertikalne ( FAycap F sub cap A y end-sub

Uklještenje (Konzola): Potpuno fiksna veza koja sprečava i pomeranje i rotaciju. Zamenjuje se sa dve komponente sile ( FAxcap F sub cap A x end-sub FAycap F sub cap A y end-sub ) i momentom uklještenja ( Mukcap M sub u k end-sub ) koji sprečava obrtanje. Osnovni koraci za rešavanje zadataka

Da biste uspešno rešili zadatak iz statike, pratite ovaj provereni postupak:

Oslobađanje od veza: Nacrtajte telo slobodno od podloge, a na mestima oslonaca ucrtajte njihove reakcije.

Razlaganje kosih sila: Sve kose sile razložite na horizontalne ( ) i vertikalne ( ) komponente. Postavljanje jednačina ravnoteže: Sum svih horizontalnih sila mora biti nula: Suma svih vertikalnih sila mora biti nula: Suma momenata za proizvoljnu tačku mora biti nula: Primer 1: Prosta greda sa nepokretnim osloncem Zadatak: Horizontalna greda dužine ima nepokretni oslonac u tački i pokretni u . Opterećena je vertikalnom silom na sredini raspona. Analiza: U tački imamo reakcije FAxcap F sub cap A x end-sub FAycap F sub cap A y end-sub , a u tački samo vertikalnu reakciju FBcap F sub cap B Rešenje: (jer nema horizontalnih spoljnih sila). Primer 2: Uklješteni nosač (Konzola) Zadatak: Homogena konzola dužine uklještena je u zid u tački . Na njenom kraju deluje vertikalna sila Analiza: Uklještenje u pruža otpor FAycap F sub cap A y end-sub Mukcap M sub u k end-sub Rešenje: Gde pronaći još materijala?

Za dodatno vežbanje i učenje, preporučujemo resurse koji nude detaljne statičke dijagrame (transverzalne i aksijalne sile, napadni momenti):

Scribd - Statika Zadaci: Velika baza zadataka sa gredama i konzolama.

YouTube - Ognjen Grozdanović: Video lekcije prilagođene srednjoškolskom programu fizike i mehanike.

Zbirka Nenada Lorkovića: Odličan priručnik sa rešenim ispitnim primerima.

Želite li da uradimo detaljan postupak za kontinualno opterećenje (npr. sneg na krovu) ili vas zanimaju rešetkasti nosači? AI responses may include mistakes. Learn more A1 Provjera - Određivanje Reakcija Nosača | PDF - Scribd

01. * Razred: II.G Smjer: Građevinski tehničar GRUPA A. * Predmet: Nosive konstrukcije (Statika) Učenik __________________________ Statika 1 Srednja skola Fizika

To demonstrate a "fixed" solution, here is a classic high school statics problem.

Problem: A homogeneous beam weighing $G = 200 , \textN$ and length $L = 4 , \textm$ rests on two supports, A and B. Support A is at the very left end, and support B is $1 , \textm$ from the right end. A weight $P = 500 , \textN$ hangs from the very right end. Calculate the reaction forces ($F_A$ and $F_B$) on the beam.

Solution:

Conclusion: The reaction force at A is $-100 , \textN$ (meaning the support must pull the beam down, or the setup is physically impossible without a clamp; typically in simple statics, this indicates an error in the setup or that B carries the full load plus extra. Note: If we assume simple supports, a negative value implies the beam would lift off support A unless it is bolted down.)

| Mistake | Consequence | Correction | |---------|-------------|-------------| | Forgetting the reaction moment (M_A) | Sum of moments will not be zero | Always draw (M_A) at a fixed support | | Wrong sign convention for moments | Wrong value for (M_A) | State convention clearly (e.g., CCW positive) and apply consistently | | Using incorrect distance for moment arm | Wrong moment magnitude | Measure perpendicular distance from force line of action to the pivot point | | Ignoring horizontal forces | (R_Ax) wrong | Always check (\sum F_x = 0), even if no horizontal applied loads – then (R_Ax=0) | | Adding a roller support to a fixed end without extra conditions | Over‑constrained system | Recognize statical indeterminacy – inform the instructor |

Ključna riječ: statika zadaci za srednju školu fixed