moment of inertia of a composite section about y-axis.

Problem:
Find the moment of inertia about y-axis.


Solution:

Solved Example - Cable and Determinate Frame - How to find Forces at the Internal Hinges and supports

Hi,
Consider the frame in the diagram. If the tension in the cable that runs between H and I is 50 lbs, determine the loads acting on the frame at A and at C, and on member EH.


Solution:


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Solved Example - Beam with Hinge - Shear Force and Bending Moment Diagram

Given the determinate continuous beam in the following, not that load 24k is applied at the mid-point of BC(you may define it as D.)

Plot the shear and moment diagram for the beam A-B-C.

Draw the Shear force and Bending moment diagram for the determinate beam

A cable applied with concentrated loads, find the sag - Solved Example.

Example: Given cable with three concentrated load.
If P1= 5.9 lbs, P2 = 5.9 lbs, and P3 = 10.9 lbs, Determine the reaction at E and the distances dB and dD.




If you have any doubt, please ask in the comment box.

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How to Solve a simple Truss problem using Method of Joints - solved example.

Here is the problem of a determinate truss.


And here is its joint by joint solution.

Redundant of curved(Circular) beam using Castigliano's theorem.

Hi,
Problem: The given beam consist of straight beam AC where A is fixed,  and curved(circular) beam CE. Load P is horizontal. (a) Draw Free Body diagram (b) Write moment equations for AC and CE part. (c) Write the expression to find the redundant at E, using the Castigliano's theorem for deflection.

curved/Circular beam redundant using Castigliano's theorem

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Characteristic Equation for a 4*4 Matrix (Eigenvalues)

Whenever a 4*4 matrix is given, and it is to find the characteristic equation. Always expand along the column or row, which has the maximum number of zeroes. Look for the solved example given below.
Given Matrix A is a 4*4 matrix, with 9, 7, 5 and 9 as the diagonal elements. First column contains the maximum zeroes, so expand along it. The final equation is the characteristic equation. Soling it gives 9, 5 and 7 as the eigenvalues.

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Solved - Virtual Work Method - Deflection of Beam - Propped Cantilever with Internal hinge

Hi

Consider the compound beam shown in fig. EI is constant. Use the principle of Virtual Work. Determine the displacement at point D.
Please refer the image below for the solution.

Virtual Work Method - Deflection of beam - Propped cantilever with internal hinge

Virtual Work Method - Deflection of Beam - Propped Cantilever with Internal Hinge

Solved - Moment Distribution Method -Frame with pinned and fixed ends)

hi,
The given frame has two roller supports and one fixed, support. One must know the stiffness and distribution factors to distribute the unbalanced moments. Take the following example. Solution is handwritten below.

Solved -Shear Flow equation- Wooden Beam and Nail Spacing using

Hi,
Here is an example of solved problem, when you are asked to find the shear capacity of nailed wooden beams, or asked about the spacing of nails. Leave your suggestions or doubts in the comment box below.

Problem: The two cross sections (a) and (b) of a wooden beam are shown below. Both are subjected to a vertical shear force of V. Each nail can support a shear force of 20 kN, and are spaced at 125 mm along the length of the beam. Section details:
a= 250 mm, b= 35 mm, c= 265 mm, d = 180 mm, and e= 300mm. Assume the sections are uniform along the length of the beam. Find:
(A) Maximum applicable shear force on member (a)
(B) Maximum applicable shear force on member (b)
(C) Adjust the spacing of the weaker member for the maximum of the forces found in part (A) and part (B).

Solution:


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Solved- ILD(Influence Line Diagram) - Shear Force and Bending Moment Overhang Beam

Hi,

The overhang beam shown is pinned at A and roller supported at B. Using equilibrium approach, derive and draw the influence line for
(a) horizontal and vertical support reactions at A.
(b) the vertical support reaction at B.
(c)The shear at C.
(d)The moment at C.

Force method for Indeterminate continuous Beam - Matrix Approach

Hi,
In force method of structural analysis,

• the first step is to find the Redundancy/indeterminacy of the structure. For example for the given beam in the following example there are total five number of support reactions, therefore the redundancy is 2.
• Second step is to convert the indeterminate structure into a basic determinate by replacing the the two of the unknown support reactions with redundants.  
• Third step is to find out the displacements of the basic determinate structure along the redundants due to the given loading conditions. 
• fourth step is to find out the flexibility matrix by applying the unit loads along the redundants and finding out the corresponding displacements at these two places.
• Next, form the equations as per the compatibility conditions and form the matrices. 
• Solve the matrix problem to find out the unknown reaction forces.

Example: Let us consider a continuous beam with a total span of 10m, EI constant, udl acting on the first half and a couple acting at 7.5m from the left. There are hinge and roller support at B and C, while beam is fixed at the left end A. Find out the support reactions at B and C using the force method (matrix approach.)

Solution: 

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Tension member connected to Gusset plate(fail in Rupture/Fracture or yield?)

Hi,
A tension member - a rectangular plate of dimension 1/2"*8" connected with two rows of bolts, determine the bolt size so that the tension member fails in rupture but not yield. Steel of grade A36 grade is used.
It must be kept in mind that the capacity factors are different for the rupture and yield, its lower for finding the rupture capacity, the section where bolts are inserted into the member are considered critical. Solution is written in the image shown below.