# Civil Engineering - Bar Question

• deon0783
In summary: Plugging in the values for a, b, c, d, u, P, and EI, we get the following solution:Axial force at point A (kN, tension positive): 0.688 Displacement at point A (mm, positive to right): 3.125In summary, the solution to this problem involves integrating the governing differential equation and applying the appropriate boundary conditions to find the axial force and displacement at point A. The result is an axial force of 0.688 kN in tension and a
deon0783
Member advised to use the homework template for posts in the homework sections of PF.
Hey everyone,

I'm at my limits here trying to solve a question, I can't seem to figure out how the lecturer gets the solution to the following problem...

Can someone please direct me the correct methodology or better yet give me some guidance on what to do? Thank you.

The Questions and solutions are:
Axial force at point A (kN, tension positive): 0.688
Displacement at point A (mm, positive to right): 3.125

Analyse the statically indeterminate bar illustrated below by integrating the governing differential equation to find the axial force and displacements, applying the boundary conditions appropriately. Find the axial force and the displacement at point A. The cross section of the bar is constant with EA = 10000 kN. a = 2.0 m, b = 1.5 m, c = 2.5 m and d = 2.0 m. w = 4 kN/m, and P = 5 kN. The bar is also subjected to a temperature increase at the time the load is applied. This temperature change varies linearly along the length of the bar and is T1 = 50 °C at the left hand end of the bar and T2 = 90 °C at the right hand end (the coefficient of thermal expansion at = 5.0e-06°C-1). The support indicated undergoes a prescribed displacement of u = 4 mm.

The diagram can be found here; http://imgur.com/a/8a1oA

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Solution:Axial force at point A (kN, tension positive): 0.688 Displacement at point A (mm, positive to right): 3.125The solution to this problem can be found by integrating the governing differential equation for the bar, applying the boundary conditions appropriately. The governing differential equation is given by: EI*(d2w/dx2) = P - w(x)where EI is the flexural rigidity of the bar, P is the applied load and w(x) is the distributed load along the length of the bar. The boundary conditions for this problem are: At x = 0: w(0) = 0 At x = a: dw/dx = 0 At x = b: dw/dx + u = 0 At x = c: w(c) = 4kN/m At x = d: dw/dx = 0Using these boundary conditions, we can integrate the governing differential equation to find the axial force and displacement at point A. First, we integrate the differential equation from x = 0 to x = a. This gives us: w(x) = P/EI * [x^3/6 - a^2x/2 + a^3/6] Next, we integrate the equation from x = a to x = b. This gives us: w(x) = P/EI * [x^3/6 - a^2x/2 + a^3/6 - (x-a)^3/6 + (x-a)u] Now, we integrate the equation from x = b to x = c. This gives us: w(x) = P/EI * [x^3/6 - a^2x/2 + a^3/6 - (x-a)^3/6 + (x-a)u - (x-b)^2(4 - u)/2] Finally, we integrate the equation from x = c to x = d. This gives us: w(x) = P/EI * [x^3/6 - a^2x/2 + a^

## 1. What exactly is civil engineering?

Civil engineering is a branch of engineering that deals with the design, construction, and maintenance of the built environment, including structures such as buildings, roads, bridges, dams, and airports. It also includes the development of infrastructure systems such as water supply, sewage treatment, and transportation networks.

## 2. What are the main responsibilities of a civil engineer?

A civil engineer is responsible for designing, planning, and overseeing the construction of various projects related to the built environment. They are also responsible for ensuring the safety, functionality, and sustainability of these projects. Other responsibilities may include budgeting, project management, and collaborating with other professionals.

## 3. What skills are essential for a successful career in civil engineering?

Some important skills for a civil engineer include strong mathematical and analytical skills, attention to detail, problem-solving abilities, and good communication skills. They should also have a good understanding of engineering principles and be able to use various software and tools for design and analysis.

## 4. How long does it take to become a licensed civil engineer?

The process of becoming a licensed civil engineer can vary depending on the country or state you are in. In general, it involves obtaining a bachelor's degree in civil engineering, gaining relevant work experience, and passing a licensing exam. This process can take anywhere from 4 to 8 years.

## 5. What are the current challenges facing civil engineering?

Some of the current challenges facing civil engineering include the need for sustainable and environmentally friendly designs, the use of new technologies and materials, and the aging infrastructure in many countries. There is also a growing focus on resilience and disaster preparedness in the face of natural disasters and climate change.

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