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

Types of Connection

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Think!

Lecture 2 4

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

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

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?

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?

Try! (FBD)

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Draw the FBD if P = 1500 N

Solution

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FBD = 5905.36 NCx = 2952.68 NCy= 3614.20 NC = 4666.98 N

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.

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

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

Internal Forces: Example

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Calculate the VC, NC and MC and their direction

Example 1.1

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

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

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