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Diagrama de Corte e Momento Fletor: Resolução de Problemas
Quando se analisa uma viga que suporta cargas concentradas e uma carga distribuída, desenhar os diagramas de corte e momento fletor é essencial. Esses…
Considere uma viga que suporta duas cargas concentradas e uma carga distribuída. Desenhe o diagrama de momento de corte e flexão para a viga.
Primeiro, desenhe um diagrama de corpo livre da viga e, usando a equação de equilíbrio, as forças de reação são obtidas.
Em seguida, divida a viga em diferentes seções e desenhe o diagrama de corpo livre de cada seção. Aplicando a equação de equilíbrio para as seções, o cisalhamento para seções individuais pode ser determinado.
O cisalhamento permanece constante entre cargas concentradas e forças de reação, enquanto varia linearmente com uma inclinação constante na seção de carga distribuída.
A área sob a curva de cisalhamento entre dois pontos é igual à mudança no momento fletor entre os mesmos dois pontos.
Considerando o momento fletor zero na extremidade da viga e recordando a relação entre a variação do momento fletor e a área sob a curva de cisalhamento, calcula-se o momento fletor em cada ponto.
O diagrama do momento fletor é desenhado conectando os pontos conhecidos com linhas retas para regiões com cisalhamento constante e uma linha parabólica para regiões com cisalhamento linear.
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Q1: What is the first step in drawing shear and bending moment diagrams?
Start by drawing a free-body diagram of the entire beam, including all concentrated loads, distributed loads, and reaction forces at the supports. Apply equilibrium equations (sum of forces and moments equal zero) to determine the reaction forces. This foundation is essential before analyzing internal forces in different sections.
Q2: How does shear force behave in different sections of a loaded beam?
Shear force remains constant between concentrated loads and reaction forces, creating horizontal segments on the shear diagram. In sections with a distributed load, shear varies linearly with a constant slope. Understanding this relationship between the distributed load and shear helps predict diagram shape without calculating every point.
Q3: Why is the area under the shear curve important for finding bending moments?
The area under the shear curve between two points equals the change in bending moment between those same points. This relationship allows you to calculate bending moments at various locations by integrating shear values. Starting from a known bending moment (typically zero at a free end), you can determine moments throughout the beam.
Q4: How do you divide a beam into sections for analysis?
Divide the beam based on load distribution: create separate sections between concentrated loads, between concentrated loads and reaction forces, and within distributed load regions. Draw a free-body diagram for each section and apply equilibrium equations to calculate shear forces. This systematic approach ensures accurate internal force determination across the entire beam.
Q5: What shapes appear in a bending moment diagram?
Connect known bending moment points with straight lines in regions where shear is constant, and parabolic curves in regions where shear varies linearly. The diagram shape reflects the underlying shear distribution: constant shear produces linear moment segments, while linear shear produces parabolic segments, creating a visual representation of internal moment distribution.
Q6: Why is sectioning the beam necessary for solving shear and bending moment problems?
Sectioning isolates portions of the beam to reveal internal forces and moments at specific locations. By drawing free-body diagrams of each section and applying equilibrium equations, you can calculate shear and bending moment values that vary along the beam's length. This method transforms a complex problem into manageable steps for internal loadings structural members problem solving.
Q7: How do concentrated loads affect the shear diagram?
Concentrated loads create vertical jumps in the shear diagram at their points of application. The magnitude of each jump equals the load value, and the direction indicates whether the load acts upward or downward. Between concentrated loads, shear remains constant, producing horizontal segments that simplify diagram construction and interpretation.