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Static Analysis
Static Analysis, Internal Forces, Stresses: Normal and Shear
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Static Analysis
Equation of equilibrium
If only x-y plane
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000 zyx FFF
000 zyx MMM
00 yx FF
0M
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Types of Connection
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Think!
Lecture 2 4
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FBD: Structure
Lecture 1 5
Discuss the approach?
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i) Equilibrium on the whole system ii) Equilibrium on Pin A
iii) Equilibrium on Pin Civ) Equilibrium on Pin D
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Take Note of the tension and compression on the members
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Two and three force body member
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Three-Force member
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Two force member determination will set the direction of FAB
Then, equilibrium equation will solve FBD: FAB, Cx and Cy
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Find the forces on each member
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Discuss the approach?
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Method 1: From Pin to Pin (equilibrium)
Question: Can we solve the problem by treating the whole system as the initial FBD?
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Discuss the approach?
Lecture 1 12
Use your engineering judgment?1) What is the direction of the force at C?2) If the downward force 0.75P is removed, which frame should be removed?
Use your engineering judgment?Does length of frame has the effect on the force calculation?
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Try! (FBD)
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Draw the FBD if P = 1500 N
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Solution
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FBD = 5905.36 NCx = 2952.68 NCy= 3614.20 NC = 4666.98 N
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Discuss the approach?
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Internal Forces
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Considering the external and internal forces; the most critical is PBC = 30 kN.
Therefore, by knowing the external and internal forces, we can decide the most critical part to be further analyzed.
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Internal Forces
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m = 500 kg
Find the internal forces at point E
Solve the FBD first
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0AM
solve FCD
0XF 0YF
Solve Ax and Ay
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Internal Forces
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0EM
solve ME
0XF 0YF
Solve VE and NE
Similar from Point B to E, apply the equilibrium equation to calculate the internal forces
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Internal Forces: Example
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Calculate the VC, NC and MC and their direction
Example 1.1
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Normal Stress
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A
Pave P: force that is perpendicular to plane
( the force is acted on the center of designated area)A: area of the plane
Calculate the average normal stress:
Structure (Assume P = 100 kN )Wide Flange Structure: W310 x 74Angles L203 x 203 x 19.0
d = 200 mm
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Allowable Normal Stress
• The allowable stress is the maximum stress allowed due to the properties of the material.
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aveall Considered as SAFE
aveall Considered as FAIL
ave
allSF
.Safety FactorSafe F.S >= 1Fail F.S < 1
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Solve it
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A load W is supported by a 3‐cable systemas shown in figure 1. The cable run along 2pulleys F and D which is attached to thesolid wall by a round beam EF and CD bothof which are 30mm diameter and 300mmlong. Ignore the mass of cable and beam. Allcables are the same size. The sizes of thepulleys at D & F can be ignored. Gravity =9.81m/s2
Answer the following questions:1.Find the internal stress at the mid point of round beam FE2.Calculate the normal stresses at cable AB, BD, BF3.Calculate the diameter of the cable is the allowable stress is 140 MPa