For Every Construction Dead load and live load is considered as the essential factor added with Soil conditions.
Site information's
Soil conditions
Size & Storage
Future Plans
Loads & Safety
Purpose & Period
Material & Budget
Infrastructure needs
Transportation, Loading & Unloading
Fabricators and contractors
Budget
Design and Detailing standards.
Entities & Key words of Truss
Bay, Beams & Column
Span or Aisle
Shallow Foundation & Piles
Bracing Systems
Chords
Rafter
Purlins
Haunch
Unbraced frames Or Portal Frames
Cladding. etc
Tensil
e stress is the normal force per area (σ = F/A) that causes an object to increase in length. Compressive stress is the normal force per area (σ = F/A) that causes an object to decrease in length.
The main difference between tensile and compressive stress is that tensile stress results in elongation whereas compressive stress results in shortening. Some materials are strong under tensile stresses but weak under compressive stresses.
The impact of your load when you step in a wooden stick causes two types of stresses, these are: Bending Stress, which is parallel to the axle of the member also called flexural stress. Shear Stress, which acts in a direction perpendicular to the axle of the member
M / I = σ /y = E / R is the formula for simple bending. The equation of pure bending is considered when bending moment is constant and shear force or rate of bending moment change is equal
Shear stress arises due to shear forces. They are the pair of forces acting on opposite sides of a body with the same magnitude and opposite direction. Shear stress is a vector quantity
Technical Key words
Compression Tensile Shear Bending Slenderness Deflection
Plane Truss: A structure that is composed of line members pin connected at the ends to form a triangulated Frame work is called a truss and if it is lie in a plane is a planar truss.
All members Centroid Straight
Centroidal Axis straight and coincident with each other
have line line of action of all loads and reaction
Top chord: Compression
Bottom Chord : Tension
There are different loads acting alternatively like bending, compressive and tensile forces and hence different combination of members combined in a truss such as beams columns purlins and rods
In a simple truss, m = 2j - 3 where m is the total number of members and j is the number of joints
If m>2j-r the excess members are called reductant members
The member forces are determined by Sequential Isolation of Joints
Basic thumb rules
quation:a2 + b2 = c2
A = span =20
B = rise=7
C = rafter length=400+49 = 21.2 feet
Pitch = 4/12base =12" rise = 4"
hypotenuse= 1.006 ft
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Base= 40ft then 1/40=1.06/x then x=42.4 roof distance
by Pythagoras 42.4sq-40sq=14.06sq = rise
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Truss count = ((roof length * 12) / 24) + 1
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There are several methods of truss analysis, but the two most common are the method of joint and the method of section (or moment).
Sign Convention
In truss analysis, a negative member axial force implies that the member or the joints at both ends of the member are in compression, while a positive member axial force indicates that the member or the joints at both ends of the member are in tension.
Analysis of Trusses by Method of Joint
This method is based on the principle that if a structural system constitutes a body in equilibrium, then any joint in that system is also in equilibrium and, thus, can be isolated from the entire system and analyzed using the conditions of equilibrium. The method of joint involves successively isolating each joint in a truss system and determining the axial forces in the members meeting at the joint by applying the equations of equilibrium. The detailed procedure for analysis by this method is stated below.
Procedure for Analysis
•Verify the stability and determinacy of the structure. If the truss is stable and determinate, then proceed to the next step. •Determine the support reactions in the truss. •Identify the zero-force members in the system. This will immeasurably reduce the computational efforts involved in the analysis. •Select a joint to analyze. At no instance should there be more than two unknown member forces in the analyzed joint. •Draw the isolated free-body diagram of the selected joint, and indicate the axial forces in all members meeting at the joint as tensile (i.e. as pulling away from the joint). If this initial assumption is wrong, the determined member axial force will be negative in the analysis, meaning that the member is in compression and not in tension. •Apply the two equations ΣFX=0Σ��=0 and ΣFY=0Σ��=0 to determine the member axial forces. •Continue the analysis by proceeding to the next joint with two or fewer unknown member forces.
Static Indeterminacy/Partial Constraint A truss is internally indeterminate
if: m > 2j – 3 (for planar trusses) where m = no. of members
m > 3j – 6 (for space trusses) where j = no. of joints
A truss is improperly constrained if: m < 2j – 3 (for planar trusses) where m = no. of members
m < 3j – 6 (for space trusses) where j = no. of joints
Procedure 1). Draw a FBD of the entire truss showing the reaction forces at the supports and the external loads. Write the equilibrium equations and solve for as many unknowns as possible.
2). Identify any zero-force members and any members that carry the same load as other members or external loads.
3). Draw a FBD of each joint in the truss. Be sure to abide by Newton’s Third Law (reactions between interacting members are equal and opposite).
4). Make a plan for solving the member loads. Start with the joint with the least number of unknowns (this frequently occurs at the supports). In solving the equilibrium equations, avoid joints that have more than two unknowns acting on it. Remember that since the forces at each joint are concurrent (i.e., they intersect at the joint), only two equilibrium equations can be utilized ( Fx 0 and Fy 0 , no moment equation exists). 5). When through solving, go back and state whether each member is in tension or compression. (That is, if a negative value is found for a member. Then you assumed the wrong direction). HINT: When drawing the FBDs of the joints, assume all members are initially in tension (i.e., show all member forces acting away from the joint). Then, if load is positive member is in tension. if load is negative member is in compression.
Determine the truss span and spacing
Determine the design loading on the truss
Choose the structural depth of the truss to control deflection
Choose the structural members which make up the truss
Check the truss for strength requirements
Calculating Live load and Dead loads
Serviceability and Deflection
Given the roof slope and the sheeting profile selected by the architect, a deflection limit of SPAN/400 has been imposed to prevent water ponding on our roof. This gives us the following deflection limit we need to aim for…
Deflection We know this already, our deflection limit is 50mm or 1.97 inch
W - Uniformly distributed load. This is also known and is 10.95 kN/m for our serviceability case (or 0.75 kps/ft)LLength of the spanning member. We know this one also, 20m or 65.6 foot
E Young’s Modulus. This is a measure of the materials stiffness, we will be designing a steel truss, generally this is taken as 200,000MPa for steel (or 29,007 kip/sq in)
I Second Moment of Inertia (or the Second Moment of Area) this is a measure of the members stiffness based on its geometry. The deeper the cross-section of the member the stiffer is it.
Moment of Inertia
Selection Of Member
Arriving Built up Depth
Truss bays and vertical members and load calculating
Axial compression and Axial tension
Verify your design to make sure it correct
Verify the stability of your structure.
We arrive at truss height and spacing.
Then we get truss span and rise
Truss count = ((roof length * 12) / 24) + 13.
Then we should sketch No of purlins
tan Alpha = rise/ (spacing of roof/2)
length of rafter = sq (l/2sq+ rise sq)
How the No of purlins Determined?
How the purlin size determined?
How the size of rafter beam , roof beam and tie beam decided?
if: m > 2j – 3 (for planar trusses) where m = no. of members
m > 3j – 6 (for space trusses) where j = no. of joints
( Fx 0 and Fy 0 , no moment equation exists). When through solving, go back and state whether each member is in tension or compression. (That is, if a negative value is found for a member. Then you assumed the wrong direction). HINT: When drawing the FBDs of the joints, assume all members are initially in tension (i.e., show all member forces acting away from the joint). Then, if load is positive member is in tension. if load is negative member is in compression.
For each action there is an equal and opposite reaction (i.e.,
FABody 1 FABody 2 ).
Assumptions for Modeling
1). All members are straight.
2). All connections are modeled as pin joints.
3). The centerlines of all members must be concurrent at the
joint.
4). External loads act only at the joints.
5). Weight of members is negligible compared with external
loads.
Identifying load type compression or Tensile.
the truss is designed based on dead load and live load,
Live load such as dead load live load wind load, snow load.
Generally this dead loads of member are calculated as rough member
from weight calculated
Weight of roofing area + weight of purlins+ weight of Self roof truss + Serviceability = Dead load
Live load of area taken from data sheet/ it should compromise years of usage and snow load if required.
Roughly members are chosen according to the cost plan.
Then it should compromise compression, tension and bending forces as per limits.
Then Every thing is rearranged and material chosen accordingly
Generally for given cost and roof dimensions members are taken from proven data's already exist.
Roof design
I feel there should be ratio in between live load, dead load and roof spacing
Truss Design
I feel there should be a ration between the dead load , storage needs and loading needs.
There should be a ratio of total loads, spacing and Primary member size
There should be a ratio between total loads roof spacing and secondary member size.
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Back again to calculating Slope and Deflection
Deflection is the transverse deformation that may occur due to shear force and bending moment. A slope is defined as the angle between the original axis and the tangent at the section
Depending on the support and loading conditions, there are different formulas for different conditions. Generally, deflection is calculated using the deflection differential equation.
d² y/dx² = M/EI
Deflection of beams is important for calculating a structure's weight and how it impacts the supporting beams. The stability of a building's floors depends on a beam, and excessive movement might affect the structure of the building.
The size, composition, weight, and positioning of any objects that are placed on the beam affect the deflection of beams. If a heavy object is positioned farthest from the location where the beam is supported or fastened to the building, the beam will deflect more.
Where slope is zero, beam deflection reaches its maximum. The angle between the actual beam at the same spot and the deflected beam is known as the slope of the beam.
4
Deflection = 5WL /384EI
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Thus, the virtual work expression for the deflection of a truss can be written as follows:
where
1 = external vertical virtual unit load applied at joint F.
n = internal axial virtual force in each truss member due to the virtual unit load, Pv = 1.
N = axial force in each truss member due to the real loads P1, P2, and P3.
∆ = external joint displacement caused by the real loads.
δL = deformation of each truss member caused by the real loads.
Procedure for Determination of Deflection in Trusses by the Virtual Work Method
•Determine the support reactions in the real system with the applied loads using the equations of equilibrium. •Determine the internal forces N in truss members caused by the external loads on the real system. •Remove all the external loads on the real system and apply a virtual unit load on the joint in the truss in the direction of required deflection. •Determine the internal virtual forces n in the members of the truss caused by the external virtual unit load placed in the joint where the deflection is desired.
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Before going to Selection of members
force (V)= R1-P1-P2
R= Resultant force
M= Bending Moment
When beam bulge is upward positive and bulge is downwards negative bending
bending moment
dM= Vdx
V = dM/dx
Σ M0 = M- (M+dM)+Vdx-wdx (dx/2)= 0
w= w/unit length
V=dM/dx
w= -dV/dx
Important points in the Shearing force and Bending moment
The algebraic sum of all the forces including reactions must be zero
Total upwards force = total download force
Σ MY = 0
The algebraic sum of the moments of all the forces including reactions about any point is zero
total clockwise moment =total anti clock wise moment
Σ M0 = 0
At hinged joint can take up load but cannot withstand any moment
At the free end of a beam (cantilever or overhanging) moment is always zero
At the simply supported ends of a beam moment is always zero.
Now I should find how force direction determined and load type finalized to have clear idea for analysis of roof truss and selection of member and the final calculations.
THE LOAD TYPES AR CONCURENT, COPLANAR OR PARRALLEL
the direction is achieved by calculating the load applied , resultant force, and load at the point and calculating we will get to know tensile and compression.
Load type is two type
Concentrated load
Applied Load
This is a case only with Concentrated Load
Serviceability Design: Serviceability Design is the consideration of deflection and vibration of a structural member. For our example we will be focusing on deflection as the roof is non-trafficable so vibration is not as much of a concern for this application.
Ultimate Design: Ultimate Design (or strength design) is consideration of a structural members strength (bending, shear, torsion, tension or compression).
You will need to consult your local design code to determine what safety factors are require for Dead an Live loading for both Ultimate and Serviceability design. In Australia the safety factors can be found in AS1170.0 Chapter 4.
Here is a summary of our safety factors taken from AS1170.0 (design factors in different regions are quite similar to these):
Loading Ultimate Serviceability
Dead Load 1.2 kN/m 1.0kN/m
Live Load 1.5 kN/m 0.7kN/m
Ex: Dead+Live 11.7 kN/m 14.9kN/m
Now deflection calculated from formula
Deflection We know this already, our deflection limit is 50mm or 1.97 inch
W - Uniformly distributed load. This is also known and is 10.95 kN/m for our serviceability case (or 0.75 kps/ft)LLength of the spanning member. We know this one also, 20m or 65.6 foot
E Young’s Modulus. This is a measure of the materials stiffness, we will be designing a steel truss, generally this is taken as 200,000MPa for steel (or 29,007 kip/sq in)
I Second Moment of Inertia (or the Second Moment of Area) this is a measure of the members stiffness based on its geometry. The deeper the cross-section of the member the stiffer is it.
We are selecting a member as planned per cost size and need of truss theough experience
and taking its IY and area of cross section and equating to
4
Deflection = 5WL /384EI to get deflection overall
then we find deflection of member
2
I OVERAL =Σ 1 to n [I n + (A n + D n )]
I = over all deflection
n is the first member
I n = deflection of the member y axis
A - Area of cross section of the member from table
The moment of inertia can be derived as getting the moment of inertia of the parts and applying the transfer
2
formula: I = I0 + Ad . We have a comprehensive article explaining the approach to solving the moment of inertia.
2
I OVERAL = [I n + (A n + D n )]
Types of Frames
Simply supported both ends
One end pin or hinged other roller
One end pin or hinged other smooth surface
Both ends fixed.
Analysis of Truss
Methods of Joints
Methods of Sections
Graphical Solution method
One end pinned and other roller - analytical method
calculations starts from left keeping pin end
Beam Rests on supports:
content/uploads/sites/13/2018/10/LectureNotes_Period_21-min.pdf
https://structville.com/2021/04/deflection-of-trusses-worked-example-2.html#:~:text=The%20deflection%20of%20roof%20trusses,adequate%20for%20all%20practical%20purposes.
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ref
https://structville.com/2021/04/deflection-of-trusses-worked-example-2.html#:~:text=Deflection%20of%20trusses%20can%20be,adequate%20for%20all%20practical%20purposes.
https://sheerforceeng.com/how-to-design-a-truss/
https://www.purdue.edu/freeform/statics/wp-content/uploads/sites/13/2018/10/LectureNotes_Period_21-min.pdf
https://eng.libretexts.org/Bookshelves/Mechanical_Engineering/Introduction_to_Aerospace_Structures_and_Materials_(Alderliesten)/02%3A_Analysis_of_Statically_Determinate_Structures/05%3A_Internal_Forces_in_Plane_Trusses/5.06%3A_Methods_of_Truss_Analysis
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