A simply supported span (middle span) of 6-m length with double cantilever of 1.5 m at each end is loaded as shown below. There is a concentrated moment of 6 kN-m acting at the tip of the left cantilever and a point load of 3 kN acting at the tip of the right cantilever. A concentrated force P = 10 kN is acting at the mid-point of the middle span. In addition, there are two partial uniform load of 5 kN/m acting on the middle span as shown below. The middle span has an I-section, of which the value of the moment of inertia I is given. The dimensions of the two flanges and the vertical web are also given. The right cantilever has a T-section. The dimensions of the top flange and the web are given. a).Calculate the maximum bending stress of the middle span and plot the bending stress distribution. The middle span is an I-section and the value of moment of inertia I is given as shown above b.) Calculate the maximum shear stress of the middle span and the shear stress at the interface between the top flange and the web of the I-section. Plot the shear stress distribution.
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
A simply supported span (middle span) of 6-m length with double cantilever of 1.5 m at each end
is loaded as shown below.
There is a concentrated moment of 6 kN-m acting at the tip of the left cantilever and a point load
of 3 kN acting at the tip of the right cantilever. A concentrated force P = 10 kN is acting at the
mid-point of the middle span. In addition, there are two partial uniform load of 5 kN/m acting on
the middle span as shown below.
The middle span has an I-section, of which the value of the moment of inertia I is given. The
dimensions of the two flanges and the vertical web are also given.
The right cantilever has a T-section. The dimensions of the top flange and the web are given.
a).Calculate the maximum bending stress of the middle span and plot the bending stress distribution.
The middle span is an I-section and the value of moment of inertia I is given as shown above
b.) Calculate the maximum shear stress of the middle span and the shear stress at the interface
between the top flange and the web of the I-section. Plot the shear stress distribution.
c)Calculate the horizontal shear flow along the interface between the top flange and the web of the
T-section of the right cantilever span. If the T-section is formed by nailing flange segment to web
segment and each nail can take a maximum of 2 kN of transverse shear force, calculate the
number of nails required for the T composite section and at what spacing should the nails be
placed
d.) If the allowable bending stress in the middle span is limited to 70 MPa, what is the maximum
value allowed for the concentrated load P at the middle span if the rest of the loadings remain
unchanged
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