Strema Notes
Strema Notes
Strema Notes
1. ST R E SS
2. ST R AI N
3. MAT E R I AL PR OPE R T I E S
4. AXI AL L OADI NG
5. T OR SI ON
6. ST R E SSE S I N B E AMS (bE ND IN G , TRAN SVERSE SHEAR)
7. COMB I NE D L OADI NGS
8. ST R E SS AND ST R AI N T R ANSFORM ATION
9. DE FL E CT I ON OF B E AMS
10. I NDE T E R MI NAT E B E AMS
11. B U CKL I NG OF COL U MN
CHAPTER 1: STRESS
1. INTRO DUCTIO N
2. C O NCE P T O F STRE SS
3. SIMP LE STRUCTURAL DE SIGN
4. NO RMAL STRE SS
5. SHE ARING STRE SS
6. BE ARING STRE SS
7. T HIN-WALLE D P RE SSURE VE SSE LS
8. SP HE RICAL SHE LL
9. STRE SSE S O N AN INCLINE D P LANE
1.1 INTRODUCTION
1.2 CONCEPT OF STRESS
1.3 SIMPLE STRUCTURAL DESIGN
1.5 SHEAR STRESS
LONGITUDINAL STRESS
region o to a
The diagram begins with a straight line from the origin O to point A, which means that the relationship
between stress and strain in this initial region is not only linear but also proportional (HOOKE’s LAW). Beyond
point A, the proportionality between stress and strain no longer exists; hence the stress at A is called the
proportional limit.
region a to b
With an increase in stress beyond the proportional limit, the strain begins to increase more rapidly for each
increment in stress. Consequently, the stress-strain curve has a smaller and smaller slope, until, at point
B, the curve becomes horizontal. Beginning at this point, considerable elongation of the test specimen occurs
with no noticeable increase in the tensile force (from B to C). This phenomenon is known as yielding of the
material, and point B is called the yield point. The corresponding stress is known as the yield stress of the
steel.
region b to c
In the region from B to C. the material becomes perfectly plastic, which means that it deforms without an
increase in the applied load.
region c to d
After undergoing the large strains that occur during yielding in the region BC, the steel begins to strain
harden. During strain hardening, the material undergoes changes in its crystalline structure, resulting in
increased resistance of the material to further deformation. Elongation of the test specimen in this region
requires an increase in the tensile load, and therefore the stress-strain diagram has a positive slope from sometimes the yield stress is not very clear
C to D. The load eventually reaches its maximum value, and the corresponding stress (at point D) is called in the diagram, it this type of diagram we
can use the o.2% offset method to determine
the ultimate stress. the yield stress. kuhanin natin yung 0.2%
sa strain axis. then draw tayo straight line
region d to e parallel sa HOOKE’S LAW LINE. YUNG POINT NG
INTERSECTION NG DIAGRAM AT NG DRAWN LINE
Further stretching of the bar is actually accompanied by a reduction in the load, and fracture finally occurs AY YUNG YIELD STRESS.
at a point such as E.
STRAIN ENERGY
DURING DEFORMATION, THE MATERIAL WILL ABSORB ENERGY, AND THE MATERIAL WILL STORE THE ENERGY
INTERNALLY IN ITS VOLUME. THIS ENERGY IS CALLED STRAIN ENERGY.
TENSILE
“PWASAN”
COMPRESSIVE
1. ALWAYS POSITIVE
2. DIMENSIONLESS
3. VALUE FROM 0 TO 0.5
CHAPTER 4: AXIALLY LOADED MEMBERS
1. SAINT- V E NANT’S PRINCIPL E
2. AXIAL DE F O RMATIO N
3. STATICALLY INDETERMINATE
AXIAL L Y L O ADE D ME MB E R
4. THE RMAL STRE SS
4.2 AXIAL DEFORMATION
4.3 STATICALLY INDETERMINATE AXIALLY LOADED MEMBER
4.4 THERMAL STRESS
CHAPTER 5: TORSION
1. TORSIONA L DEFORMATION
OF CIRCULAR SHA FT
2. POWER TRANSMISSION
3. ANGLE OF TWIST
4. STATICA LLY INDETERMINATE
5. TORQUE LOA DED MEMBER
CHAPTER 6: STRESSES IN BEAMS
1. BE NDI NG STR E SS
2. T R ANSVE R SE SH E AR
3. D E SI G N OF B E AM
4. RE I NFOR C E D B E AM S
CHAPTER 7: COMBINED LOADINGS
1. S tresses caused by combined
loadings
CHAPTER 8:
STRESS AND STRAIN TRANSFORMATION
1. STRESS TRANSFORMATION
GENERAL EQUATIONS
2. PRINCIPAL STRESSES
3. MAXIMUM IN-PLANE SHEAR STRESS
4. MOHR’S CIRCLE FOR PLANE STRE SS
5. PLAIN STRAIN TRANSFORMATION
CHAPTER 9: DEFLECTION OF BEAMS
1. D OUB L E IN T E GR A T ION M E T H O D
2. A RE A -M O M E N T M E T H OD
3. C O N JU G A T E B E A M M E T H OD
4. C A ST IGL IA N O ’S T H E OR E M
5. M ET H OD OF SU PE R PO SIT ION
6. three-moment equation
7. virtual work method
deflection of beams 9.1 double-integration method
definition of deflection definition of Double-integration method
>> The degree to which a structural element is displaced under load. It may >> The double-integration method is a useful tool in solving deflection of
refer to an angle or distance. a beam at any point by finding the equation of the elastic curve.
>> The vertical displacement of the centroid of each beam cross section with
respect to its original position. euler-bernoulli equation
assumptions
1. Elastic >> ability of a deformed body to return to its original shape.
2. Negligible axial loading >> insignificant when compared to SF and BM.
3. Small deformation >> relatively small.
In calculus, the radius of curvature of a curve y=f(x) is given by rho.
>> Consider two points m 1 and m 2 . These points are distance ds apart. The
tangents to the deflection curve at these points are lines m lp l and m 2p 2. The
normals to these tangents intersect at the center of curvature. The angle
d between the normals is given by the following equation in which r is
the radius of curvature and d is measured in radians. Because the normals
and the tangents m lp l and m 2p 2 are perpendicular, it follows that the angle
between the tangents is also equal to d .
angles between the tangents and the x axis are actually very small, we
see that the vertical distance dt is equal to x1d(theta), where x1 is the
horizontal distance from point B to the small element m1m2 . Since d(theta) RULES OF SIGN
= Mdx/EI , we obtain :
The distance dt represents the contribution made by the
bending of element m1m2 to the tangential deviation t B/A.
The expression x1Mdx/EI may be interpreted geometrically
as the first moment of the area of the shaded strip of width dx within the
M/EI diagram. This first moment is evaluated with respect to a vertical line
through point B. Integrating between points A and B, we get :
Simple Rule : If the load tends to bend the beam upward, it is above
x-axis. If the load tends to bend the beam downward, it is below x-axis.
CHAPTER 10: INDETERMINATE BEAMS
1. S T A BILIT Y A N D D ET ERMIN A CY
2. T Y PES O F IN D ET ERMIN A T E BEA M S
3. MET HOD O F IN T EGRA T ION
4. MOMEN T - A REA MET HOD
5. MET HOD O F S U PERPO S IT IO N
6. T HREE- MOMEN T EQ U A T IO N
7. MOMEN T D IS T RIBU T ION MET HO D
8. S LOPE- D EFLECT IO N MET HO D
CHAPTER 11: BUCKLING OF COLUMN
1. work in progress ___
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