## Beam Deflection Formula Stress and Deflections of Beams

Find deflection and slope of a simply supported beam with. Beam Formula вЂўShear and moment diagrams вЂўSimple beam (uniformly distributed load) вЂ“Reaction force formula вЂ“Maximum moment formula вЂўSimple beam (concentrated load at center) вЂ“Reaction force formula вЂ“Maximum moment formula. Beam Formulas вЂўSimilar loading conditions = similar shear and moment diagrams вЂўStandard formula can represent the вЂ¦, 1. The z-type deflection is a result of the vertical bending force action. 2. To find the components of the inverse stiffness tensor corresponding to the z-type deflection, one should solve the problem of the beam static deflection which is reduced to the ordinary differential equation of the second order. 3. The vertical force results in the.

### Beam Deflection How to Calculate Linear Motion Tips

The Mathematics of Simple Beam Deflection. sive tables of formulas for the calculation of stress, strain, and strength are given. Because they are not believed to serve the purpose of this book, derivations of formulas and detailed explanations, such as are appro-priate in a textbook, are omitted, but a вЂ¦, Engineering Formula Sheet Probability Conditional Probability Binomial Probability (order doesnвЂ™t matter) P k Beam Formulas Reaction B Moment x L (at point of load) Deflection x L (at point of load) Reaction L B Moment x (at center) Deflection L (at center) x Reaction B Moment x (between loads) Deflection ( L - (at center) ) Reaction L and B L Moment x L (at Point of Load) Deflection.

Chapter 6 Deflection of Beams. 6.1 Introduction Because the design of beams is frequently governed by rigidity rather than strength. For example, building codes specify limits on deflections as well as stresses. Excessive deflection of a beam not only is visually disturbing but also may cause damage to other parts of the building. For this reason, building codes limit the maximum deflection вЂ¦ Drive The Formula Of Deflection Of Beam.pdf - Free download Ebook, Handbook, Textbook, User Guide PDF files on the internet quickly and easily.

Total deflection is composed of two components: 1) Instantaneous Deflection -- when loads applied 2) Additional deflections which occur over time due to creep and shrinkage Consider first the instantaneous deflection. For moments at or below the cracking moment, the moment of inertia is that of the uncracked transformed section (Iut); E=Ec. 4. Cantilever Beam вЂ“ Uniformly varying load: Maximum intensity П‰o (N/m) Оё= П‰ol 3 24 EI y= 5. Cantilever Beam вЂ“ Couple moment M at the free end Оё= Ml EI y= BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6. Beam Simply Supported at Ends вЂ“ Concentrated load P at the

1. The z-type deflection is a result of the vertical bending force action. 2. To find the components of the inverse stiffness tensor corresponding to the z-type deflection, one should solve the problem of the beam static deflection which is reduced to the ordinary differential equation of the second order. 3. The vertical force results in the Chapter 10 Statically Indeterminate Beams 10.1 Introduction in this chapter we will analyze the beam in which the number of reactions exceed the number of independent equations of equilibrium integration of the differential equation, method of superposition compatibility equation (consistence of deformation)

BEAM DESIGN FORMULAS WITH SHEAR AND MOMENT DIAGRAMS 2005 EDITION ANSI/AF&PA NDS-2005 Approval Date: JANUARY 6, 2005 ASD/LRFD В® N DS NATIONAL DESIGN SPECIFICATIONВ® FOR WOOD CONSTRUCTION WITH COMMENTARY AND SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION American бђ‰ Forest & x Paper Association wбђ‰ вЂ¦ Beam Deflection Formula. Deflection is a degree to which a particular structural element can be displaced by a considerable amount of load. It can be referred to as an angle or the distance. The distance of deflection of a member under a load is directly related to the slope of deflected shape of the member under that load. It can be calculated

Because the beam is pinned to its support, the beam cannot experience deflection at the left-hand support. вЂў w(L)=0 . The beam is also pinned at the right-hand support. вЂў w''(0)=0 . As for the cantilevered beam, this boundary condition says that the beam is free to rotate and does not experience any torque. In real life, there is usually a Bending Deflection вЂ“ Statically Indeterminate Beams AE1108-II: Aerospace Mechanics of Materials Aerospace Structures & Materials Faculty of Aerospace Engineering Dr. Calvin Rans Dr. Sofia Teixeira De Freitas. Recap I. Free Body Diagram II. Equilibrium of Forces (and Moments) III.Displacement Compatibility IV.Force-Displacement (Stress-Strain) Relations V.Answer the вЂ¦

03/10/2016В В· Beam Deflection Calculator Download: https://goo.gl/UCMhou. How to Calculate the deflection of a beam? With this sheet you can calculate the deflection and angle under which a beam, bar or tube BEAM DESIGN FORMULAS WITH SHEAR AND MOMENT DIAGRAMS American Forest & Paper Association w R V V 2 2 Shear M max Moment x DESIGN AID No. 6 . AMERICAN WOOD COUNCIL The American Wood Council (AWC) is part of the wood products group of the American Forest & Paper Association (AF&PA). AF&PA is the national trade association of the forest, paper, and вЂ¦

BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM DEFLECTION 1. Cantilever Beam вЂ“ Concentrated load P at the free end 2 2 Pl EI Оё= 2 3 6 Px ylx EI = в€’ 3 max 3 Pl EI Оґ= 2. Cantilever Beam вЂ“ Concentrated load P at any point 2 2 Pa EI Оё= 2 3for0 6 Px yaxxa EI = в€’<< 2 3for 6 Pa yxaaxl EI = в€’<< 2 max 3 6 Pa la EI Оґ =в€’ 3. Cantilever Beam вЂ“ вЂ¦ BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM DEFLECTION 1. Cantilever Beam вЂ“ Concentrated load P at the free end 2 2 Pl EI Оё= 2 3 6 Px ylx EI = в€’ 3 max 3 Pl EI Оґ= 2. Cantilever Beam вЂ“ Concentrated load P at any point 2 2 Pa EI Оё= 2 3for0 6 Px yaxxa EI = в€’<< 2 3for 6 Pa yxaaxl EI = в€’<< 2 max 3 6 Pa la EI Оґ =в€’ 3. Cantilever Beam вЂ“ вЂ¦

Bending Deflection вЂ“ Statically Indeterminate Beams AE1108-II: Aerospace Mechanics of Materials Aerospace Structures & Materials Faculty of Aerospace Engineering Dr. Calvin Rans Dr. Sofia Teixeira De Freitas. Recap I. Free Body Diagram II. Equilibrium of Forces (and Moments) III.Displacement Compatibility IV.Force-Displacement (Stress-Strain) Relations V.Answer the вЂ¦ deflection curve of beams and finding deflection and slope at specific points along the axis of the beam 9.2 Differential Equations of the Deflection Curve consider a cantilever beam with a concentrated load acting upward at the free end the deflection v is the displacement in the y direction the angle of rotation of the axis

meet, (point C in the beam shown below). The deflection curve for this beam is physically continuous at point C. Therefore the deflection of point C as determined for the left and right hand part of the beam must be equal. Similarly, the slopes found for each part of the beam must be equal at point C. Beam Bending Stresses and Shear Stress Pure Bending in Beams With bending moments along the axis of the member only, a beam is said to be in pure bending. Normal stresses due to bending can be found for homogeneous materials having a plane of symmetry in the y axis that follow HookeвЂ™s law. Maximum Moment and Stress Distribution In a member of constant cross вЂ¦

Bending Deflection вЂ“ Statically Indeterminate Beams AE1108-II: Aerospace Mechanics of Materials Aerospace Structures & Materials Faculty of Aerospace Engineering Dr. Calvin Rans Dr. Sofia Teixeira De Freitas. Recap I. Free Body Diagram II. Equilibrium of Forces (and Moments) III.Displacement Compatibility IV.Force-Displacement (Stress-Strain) Relations V.Answer the вЂ¦ BEAM DESIGN FORMULAS WITH SHEAR AND MOMENT DIAGRAMS 2005 EDITION ANSI/AF&PA NDS-2005 Approval Date: JANUARY 6, 2005 ASD/LRFD В® N DS NATIONAL DESIGN SPECIFICATIONВ® FOR WOOD CONSTRUCTION WITH COMMENTARY AND SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION American бђ‰ Forest & x Paper Association wбђ‰ вЂ¦

Adding the deflection due to the uniform load and the deflection due to the applied (point) load gives the total deflection at the end of the beam: Deflection of simply supported beams. Linear shafts and actuators are often secured at their ends, leaving their length unsupported, much like a simply supported beam. The uniform load on the beam Bending Deflection вЂ“ Statically Indeterminate Beams AE1108-II: Aerospace Mechanics of Materials Aerospace Structures & Materials Faculty of Aerospace Engineering Dr. Calvin Rans Dr. Sofia Teixeira De Freitas. Recap I. Free Body Diagram II. Equilibrium of Forces (and Moments) III.Displacement Compatibility IV.Force-Displacement (Stress-Strain) Relations V.Answer the вЂ¦

Beam Formula вЂўShear and moment diagrams вЂўSimple beam (uniformly distributed load) вЂ“Reaction force formula вЂ“Maximum moment formula вЂўSimple beam (concentrated load at center) вЂ“Reaction force formula вЂ“Maximum moment formula. Beam Formulas вЂўSimilar loading conditions = similar shear and moment diagrams вЂўStandard formula can represent the вЂ¦ Bending Deflection вЂ“ Statically Indeterminate Beams AE1108-II: Aerospace Mechanics of Materials Aerospace Structures & Materials Faculty of Aerospace Engineering Dr. Calvin Rans Dr. Sofia Teixeira De Freitas. Recap I. Free Body Diagram II. Equilibrium of Forces (and Moments) III.Displacement Compatibility IV.Force-Displacement (Stress-Strain) Relations V.Answer the вЂ¦

Adding the deflection due to the uniform load and the deflection due to the applied (point) load gives the total deflection at the end of the beam: Deflection of simply supported beams. Linear shafts and actuators are often secured at their ends, leaving their length unsupported, much like a simply supported beam. The uniform load on the beam What Is The Formula Of A Deflection Cantilever Beam PointDeflection Of Beam Formula Simply Supported New ImagesDeflection Of Beam Formula Simply Supported New ImagesSlope And Deflection Of Beams CantileverDeflection Of вЂ¦

Bending Deflection вЂ“ Differential Equation Method AE1108-II: Aerospace Mechanics of Materials Aerospace Structures & Materials Faculty of Aerospace Engineering Dr. Calvin Rans Dr. Sofia Teixeira De Freitas. Recap вЂўSo far, for symmetric beams, we have: вЂўLooked at internal shear force and bending moment distributions вЂўDetermined normal stress distribution due to bending вЂ¦ BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM DEFLECTION 1. Cantilever Beam вЂ“ Concentrated load P at the free end 2 2 Pl EI Оё= 2 3 6 Px ylx EI = в€’ 3 max 3 Pl EI Оґ= 2. Cantilever Beam вЂ“ Concentrated load P at any point 2 2 Pa EI Оё= 2 3for0 6 Px yaxxa EI = в€’<< 2 3for 6 Pa yxaaxl EI = в€’<< 2 max 3 6 Pa la EI Оґ =в€’ 3. Cantilever Beam вЂ“ вЂ¦

03/10/2016В В· Beam Deflection Calculator Download: https://goo.gl/UCMhou. How to Calculate the deflection of a beam? With this sheet you can calculate the deflection and angle under which a beam, bar or tube BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM DEFLECTION 1. Cantilever Beam вЂ“ Concentrated load P at the free end 2 2 Pl EI Оё= 2 3 6 Px ylx EI = в€’ 3 max 3 Pl EI Оґ= 2. Cantilever Beam вЂ“ Concentrated load P at any point 2 2 Pa EI Оё= 2 3for0 6 Px yaxxa EI = в€’<< 2 3for 6 Pa yxaaxl EI = в€’<< 2 max 3 6 Pa la EI Оґ =в€’ 3. Cantilever Beam вЂ“ вЂ¦

EulerвЂ“Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case for small deflections of a beam that are subjected to lateral loads only. Beam Deflection Formula. Deflection is a degree to which a particular structural element can be displaced by a considerable amount of load. It can be referred to as an angle or the distance. The distance of deflection of a member under a load is directly related to the slope of deflected shape of the member under that load. It can be calculated

### Beam Deflection Tables MechaniCalc

Deflection of Beams with Special Reference to Shear. BEAM DESIGN FORMULAS WITH SHEAR AND MOMENT DIAGRAMS American Forest & Paper Association w R V V 2 2 Shear M max Moment x DESIGN AID No. 6 . AMERICAN WOOD COUNCIL The American Wood Council (AWC) is part of the wood products group of the American Forest & Paper Association (AF&PA). AF&PA is the national trade association of the forest, paper, and вЂ¦, will be followed in deflection of beam and in shear force and bending moment diagram. Here downward direction will be negative i.e. negative Y-axis. Therefore downward deflection of the beam will be treated as negative. To determine the value of deflection of beam subjected to a given loading where we will use the formula, = 2 2 x dy EI M dx..

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Deflections and Slopes of Beams Cengage. For a uniform beam total deflection of A relative to B = - x first moment of area of B.M. diagram about A Again, if B is not a point of zero slope the equation only gives the deflection of A relative to Useful quantities for use with uniformly distributed loads are shown in Fig. 5.1. 1 EI https://simple.wikipedia.org/wiki/Euler-Bernoulli_Beam_Theory Chapter 10 Statically Indeterminate Beams 10.1 Introduction in this chapter we will analyze the beam in which the number of reactions exceed the number of independent equations of equilibrium integration of the differential equation, method of superposition compatibility equation (consistence of deformation).

Engineering Calculators Menu Engineering Analysis Menu. Structural Beam Deflection, Stress Formula and Calculator: The follow web pages contain engineering design calculators that will determine the amount of deflection and stress a beam of known cross section geometry will deflect under the specified load and distribution. Chapter 10 Statically Indeterminate Beams 10.1 Introduction in this chapter we will analyze the beam in which the number of reactions exceed the number of independent equations of equilibrium integration of the differential equation, method of superposition compatibility equation (consistence of deformation)

Mechanics of Materials CIVL 3322 / MECH 3322 Deflection of Beams The Elastic Curve ! The deflection of a beam must often be limited in order to provide integrity and stability of a structure or machine, or ! To prevent any attached brittle materials from cracking 2 Beam Deflection вЂ¦ Because the beam is pinned to its support, the beam cannot experience deflection at the left-hand support. вЂў w(L)=0 . The beam is also pinned at the right-hand support. вЂў w''(0)=0 . As for the cantilevered beam, this boundary condition says that the beam is free to rotate and does not experience any torque. In real life, there is usually a

will be followed in deflection of beam and in shear force and bending moment diagram. Here downward direction will be negative i.e. negative Y-axis. Therefore downward deflection of the beam will be treated as negative. To determine the value of deflection of beam subjected to a given loading where we will use the formula, = 2 2 x dy EI M dx. Using formula 2E we have 750 x 10 6 (no units) 2 x 53.3x10 5000 x 4 2EI FL dx dy-6 2 ii. Deflection Using formula 2F we have - 0.002 m 3 x 53.3 x 10 5000 x 4-3EI FL y 6 3 The deflection is 2 mm downwards. SELF ASSESSMENT EXERCISE No.1 1. A cantilever beam is 6 m long and has a point load of 20 kN at the free end. The flexural stiffness is 110

Using formula 2E we have 750 x 10 6 (no units) 2 x 53.3x10 5000 x 4 2EI FL dx dy-6 2 ii. Deflection Using formula 2F we have - 0.002 m 3 x 53.3 x 10 5000 x 4-3EI FL y 6 3 The deflection is 2 mm downwards. SELF ASSESSMENT EXERCISE No.1 1. A cantilever beam is 6 m long and has a point load of 20 kN at the free end. The flexural stiffness is 110 Beam Deflection Formula. Deflection is the degree to which a particular structural element can be displaced by a considerable amount of load. It can be referred to an angle or distance. The distance of deflection of a member under a load is directly related to the slope of the deflected shape of the member under that load. It can be calculated by integrating the function that вЂ¦

Drive The Formula Of Deflection Of Beam.pdf - Free download Ebook, Handbook, Textbook, User Guide PDF files on the internet quickly and easily. BEAM DEFLECTION FORMULA EPUB DOWNLOAD Go Articles This page discusses the calculation of stresses and deflections in beams. diagrams, stresses in beams, and a table of common beam deflection formulas. Structural Beam Deflection, Stress Formula and Calculator: The follow web pages contain...

BEAM DESIGN FORMULAS WITH SHEAR AND MOMENT DIAGRAMS American Forest & Paper Association w R V V 2 2 Shear M max Moment x DESIGN AID No. 6 . AMERICAN WOOD COUNCIL The American Wood Council (AWC) is part of the wood products group of the American Forest & Paper Association (AF&PA). AF&PA is the national trade association of the forest, paper, and вЂ¦ Engineering Calculators Menu Engineering Analysis Menu. Structural Beam Deflection, Stress Formula and Calculator: The follow web pages contain engineering design calculators that will determine the amount of deflection and stress a beam of known cross section geometry will deflect under the specified load and distribution.

Deflections and Slopes of Beams G TABLE G-1 DEFLECTIONS AND SLOPES OF CANTILEVER BEAMS v deflection in the y direction (positive upward) vdv/dx slope of the deflection curve d B v(L) deflection at end B of the beam (positive downward) u B v(L) angle of rotation at end B of the beam (positive clockwise) EI constant 1 v 2 2 q 4 x E 2 I (6L2 4Lx x Chapter 10 Statically Indeterminate Beams 10.1 Introduction in this chapter we will analyze the beam in which the number of reactions exceed the number of independent equations of equilibrium integration of the differential equation, method of superposition compatibility equation (consistence of deformation)

4. Cantilever Beam вЂ“ Uniformly varying load: Maximum intensity П‰o (N/m) Оё= П‰ol 3 24 EI y= 5. Cantilever Beam вЂ“ Couple moment M at the free end Оё= Ml EI y= BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6. Beam Simply Supported at Ends вЂ“ Concentrated load P at the Beam Bending Stresses and Shear Stress Pure Bending in Beams With bending moments along the axis of the member only, a beam is said to be in pure bending. Normal stresses due to bending can be found for homogeneous materials having a plane of symmetry in the y axis that follow HookeвЂ™s law. Maximum Moment and Stress Distribution In a member of constant cross вЂ¦

BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM DEFLECTION 1. Cantilever Beam вЂ“ Concentrated load P at the free end 2 2 Pl EI Оё= 2 3 6 Px ylx EI = в€’ 3 max 3 Pl EI Оґ= 2. Cantilever Beam вЂ“ Concentrated load P at any point 2 2 Pa EI Оё= 2 3for0 6 Px yaxxa EI = в€’<< 2 3for 6 Pa yxaaxl EI = в€’<< 2 max 3 6 Pa la EI Оґ =в€’ 3. Cantilever Beam вЂ“ вЂ¦ The tables below give equations for the deflection, slope, shear, and moment along straight beams for different end conditions and loadings. You can find comprehensive tables in references such as Gere, Lindeburg, and Shigley. However, the tables below cover most of вЂ¦

1. The load w(x) is linearly related to the deflection v(x), 2. The load is assumed not to change significantly the original geometry of the beam of shaft. Then, it is possible to find the slope and displacement at a point on a beam subjected to several different loadings by algebraically adding the effects of its various component parts. Using formula 2E we have 750 x 10 6 (no units) 2 x 53.3x10 5000 x 4 2EI FL dx dy-6 2 ii. Deflection Using formula 2F we have - 0.002 m 3 x 53.3 x 10 5000 x 4-3EI FL y 6 3 The deflection is 2 mm downwards. SELF ASSESSMENT EXERCISE No.1 1. A cantilever beam is 6 m long and has a point load of 20 kN at the free end. The flexural stiffness is 110

Cantilever Beam вЂ“ Couple moment M at the free end Ml Mx 2 Ml 2 Оё= y= Оґ max = EI 2 EI 2 EI BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6. Beam Simply Supported at Ends вЂ“ Concentrated load P at the center Pl 2 Px вЋ› 3l 2 вЋћ l Pl 3 Оё1 = Оё2 = y= вЋњ в€’ x 2 вЋџ for BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6. Beam Simply Supported at Ends вЂ“ Concentrated load P at the center 2 1216 Pl E I (2 ) 2 2 3 Px l l for 0yx x 12 4 2 EI 3 max Pl 48 E I x 7. Beam Simply Supported at Ends вЂ“ Concentrated load P at any point 22 1 ()Pb l b 6lEI o 2 Pab вЂ¦

Adding the deflection due to the uniform load and the deflection due to the applied (point) load gives the total deflection at the end of the beam: Deflection of simply supported beams. Linear shafts and actuators are often secured at their ends, leaving their length unsupported, much like a simply supported beam. The uniform load on the beam deflection is limited to the beamвЂ™s span length divided by 250. Hence a 5m span beam can deflect as much as 20mm without adverse effect. Thus, in many situations it is necessary to calculate, using numerical methods, the actual beam deflection under the anticipated design load and compare this figure with the

Because the beam is pinned to its support, the beam cannot experience deflection at the left-hand support. вЂў w(L)=0 . The beam is also pinned at the right-hand support. вЂў w''(0)=0 . As for the cantilevered beam, this boundary condition says that the beam is free to rotate and does not experience any torque. In real life, there is usually a BEAM DEFLECTION FORMULA EPUB DOWNLOAD Go Articles This page discusses the calculation of stresses and deflections in beams. diagrams, stresses in beams, and a table of common beam deflection formulas. Structural Beam Deflection, Stress Formula and Calculator: The follow web pages contain...

CE 433, Fall 2006 Deflection of a Reinforced Concrete Beam 5 / 9 2) Effective Moment of Inertia, I e The ACI equation for effective moment of inertia (Ie) accounts for the fact that some of the reinforced concrete beam is cracked, and some of it is uncracked (as shown in Figure 3). Figure 3. The tables below give equations for the deflection, slope, shear, and moment along straight beams for different end conditions and loadings. You can find comprehensive tables in references such as Gere, Lindeburg, and Shigley. However, the tables below cover most of вЂ¦

BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM DEFLECTION 1. Cantilever Beam вЂ“ Concentrated load P at the free end 2 2 Pl EI Оё= 2 3 6 Px ylx EI = в€’ 3 max 3 Pl EI Оґ= 2. Cantilever Beam вЂ“ Concentrated load P at any point 2 2 Pa EI Оё= 2 3for0 6 Px yaxxa EI = в€’<< 2 3for 6 Pa yxaaxl EI = в€’<< 2 max 3 6 Pa la EI Оґ =в€’ 3. Cantilever Beam вЂ“ вЂ¦ Bending Deflection вЂ“ Differential Equation Method AE1108-II: Aerospace Mechanics of Materials Aerospace Structures & Materials Faculty of Aerospace Engineering Dr. Calvin Rans Dr. Sofia Teixeira De Freitas. Recap вЂўSo far, for symmetric beams, we have: вЂўLooked at internal shear force and bending moment distributions вЂўDetermined normal stress distribution due to bending вЂ¦

of elasticity of the beam material, and I is the area moment of inertia about the centroidal axis of the bearp cross section. is the temperature coefficient of expansion ( unit strain per degree) l. of elasticity of the beam material, and I is the area moment of inertia about the centroidal axis of the bearp cross section. is the temperature coefficient of expansion ( unit strain per degree) l.