# How to Conduct a Static Analysis of a Truss?

• MHB
• littlemac1
In summary: F6 = -2.25 kN.In summary, the truss sketch provided is supported by external reactions R1 = 0 kN, R2 = 3.5 kN, and R3 = 4.5 kN at joints A, B, and F respectively. To draw the free body diagrams for joints C and E, some assumptions were made and the equations for all forces acting on those joints were calculated. It was determined that the force acting on member F2 is zero and the force acting on member F5 is also zero. For joint E, the force acting on member F4 is -4.5/√3 kN and the force acting on member F6 is -2
littlemac1
Below is a sketch of a truss in which external support reactions are given as R1 = 0 kN, R2 = 3.5 kN, R3 = 4.5 kN. Members (M) are labeled in boxes, joints labeled in circles, and forces R.

Draw 2 Free body diagrams, one for each joints C and E.
Define what direction represents a positive force, and write equations for all forces acting on that joint.

View attachment 9138

For example, for joint D it's:
("SUM" is used for summation symbol)
SUMFy = 0
SUMFy = F4 sin(30) + R3 = 0
SUMFy = F4(1/2) + 4.5 kN = 0
F4 = -9kN
View attachment 9139

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I would like to provide some feedback and additional information on the truss sketch and the requested free body diagrams.

Firstly, it is important to note that trusses are commonly used in structural engineering to support loads and distribute forces. They are composed of interconnected members, which are typically straight and connected at joints. In the sketch provided, the truss is supported by external reactions R1, R2, and R3 at joints A, B, and F respectively.

To accurately draw the free body diagrams for joints C and E, some assumptions need to be made about the truss. For the purpose of this response, I will assume that the truss is in equilibrium and that all members are in tension.

For joint C, the positive force direction will be upwards, as indicated by the arrow in the sketch. The equations for all forces acting on joint C can be written as:

SUMFy = 0
SUMFy = F2 cos(30) + F5 = 0
SUMFy = F2(√3/2) + F5 = 0
F5 = -F2(√3/2)

SUMFx = 0
SUMFx = R1 + F2 sin(30) = 0
SUMFx = 0 + F2(1/2) = 0
F2 = 0

Therefore, the force acting on member F2 is zero and the force acting on member F5 can be calculated as F5 = -√3/2 F2 = 0.

For joint E, the positive force direction will be downwards, as indicated by the arrow in the sketch. The equations for all forces acting on joint E can be written as:

SUMFy = 0
SUMFy = F4 sin(30) + F6 = 0
SUMFy = F4(1/2) + F6 = 0
F6 = -F4(1/2)

SUMFx = 0
SUMFx = R3 + F4 cos(30) = 0
SUMFx = 4.5 + F4(√3/2) = 0
F4 = -4.5/√3

Therefore, the force acting on member F4 can be calculated as F4 = -4.5/√3 kN and the force acting on member F

## 1. What is static analysis of truss?

Static analysis of truss is a method used to determine the internal forces and stresses in a truss structure under static loading conditions. It involves using mathematical equations and principles of mechanics to analyze the equilibrium of the truss and determine the forces acting on each member.

## 2. Why is static analysis of truss important?

Static analysis of truss is important because it helps engineers and designers ensure that a truss structure is able to withstand the expected loads and does not fail under normal operating conditions. It also allows for optimization of the truss design to minimize material usage and cost.

## 3. What are the assumptions made in static analysis of truss?

The main assumptions made in static analysis of truss are that the truss members are connected by perfect pins, the truss is loaded at the joints, and the truss is in a state of static equilibrium. These assumptions allow for simplification of the analysis and provide accurate results for most truss structures.

## 4. How is static analysis of truss different from dynamic analysis?

Static analysis of truss only considers the effects of static loads on the structure, while dynamic analysis takes into account the effects of time-varying loads and the resulting vibrations. Static analysis is typically used for permanent structures, while dynamic analysis is more relevant for structures subjected to moving loads or seismic events.

## 5. What are the common methods used for static analysis of truss?

The two main methods used for static analysis of truss are the method of joints and the method of sections. The method of joints involves analyzing the forces at each joint of the truss, while the method of sections involves cutting the truss into smaller sections and analyzing the forces on each section. Both methods use the principles of equilibrium and compatibility to determine the internal forces in the truss members.

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