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TECHNOLOGY AND ENGINERRING SKILL DEPARTEMEN PROGRAM : BUILDING TECHNOLOGY SKILL COMPETENCE : DRAWING BUILDING TECHNOLOGY Implementing Statistics and Energy Objectives : The students are able to explain the meaning of mechanical technique and building statistics The student are able to explain the meaning of energy, resultant vector and energy moment The students are able to explain arranging and decomposition process graphically and analytically The students are able to arrange and to decompose energy graphically and analytically Technology and Reenginering Implementing Statistics and Energy The students are able to decompose energy to some energies graphically well The students count energy resultant The students are able to count energy moment The students are able to explain mean and kinds of burden on construction counting of building statistics Technology and Reenginering Implementing Statistics and Energy The students are able to know the working principal of energy action reaction The students are able to explain the working pricipal of torque coupling The stdents are able to explain the working principal of energy balance Technology and Reenginering Term of Technical Mechanic and building static OR Technology and Reenginering Term of Technical Mechanic and building static a scientific science learning about energy balance of statics constructions even though there are several working energies. Technology and Reenginering Term of Technical Mechanic and building static A scientific science learning about action of an abject without learning the cause of that action Technology and Reenginering Term of Technical Mechanic and building static A science studying about moves and cause of that move itself Technology and Reenginering Term of Technical Mechanic and building static A scientific science learning about stability and power of a building construction or parts of those building itself Technology and Reenginering Term of Technical Mechanic and building static Including Technology and Reenginering Term of Technical Mechanic and building static A calculation held to make building to be strong. In this case, a checking must be held concerning of building position together with foundation and land texture as the foundation. Technology and Reenginering Term of Technical Mechanic and building static is a calculation deciding the size of material texture needed to support power/energy working on the construction by considering security factors. Technology and Reenginering Term of Technical Mechanic and building static This kinds of calculation is very important to guarantying power and to make material ussage efficient Technology and Reenginering Term of Technical Mechanic and building static Is a calculation to check whether there are a change in shape, over limit transitioning or not. Technology and Reenginering Term of Technical Mechanic and building static a calculation to check whether the building be built strong enough to the load planned Technology and Reenginering Term of energy, vector, resultante dan energy moment Term of Energy If we are going to know what is energy, see and observe these experiences below. A ball is kicked so it will rotate, or there is a change of place of the ball. Technology and Reenginerring Term of energy, vector, resultante dan energy moment A rolling ball is kicked again, this will rotate a bit faster. It means there is a chage to the ball. Technology and Reenginerring Term of energy, vector, resultante dan energy moment A quite ball is placed in the corner of the wall. Having kicked, this ball doesn’t move at all. But, a fiew seconds there is change with ball. Technology and Reenginerring Term of energy, vector, resultante dan energy moment From the three experiences above that : “Energy is whatever things that may cause change of a place, movement or shape.” Technology and Reenginerring Term of energy, vector, resultante dan energy moment P=mxa P = energy m = weight a = speed Technology and Reenginerring Term of energy, vector, resultante dan energy moment Technology and Reenginerring Term of energy, vector, resultante dan energy moment For example 100 kgs, 1000 Newtons and 50 Tons = 100 kgs = 1000 N Technology and Reenginerring Term of energy, vector, resultante dan energy moment A target for the energy working The box is pushed on spot A, so the box will move to the right. Technology and Reenginerring Term of energy, vector, resultante dan energy moment The box is pushed on spot B, so it won’t move othetwise it plunges Technology and Reenginerring Term of energy, vector, resultante dan energy moment Both experiment pictures show that energy has a work spot Technology and Reenginerring Pengertian gaya, vektor, resultante dan momen gaya Work line is a stright line scratching with that energy itself. Technology and Reenginerring Term of energy, vector, resultante dan energy moment Work Work line line An energy can be moved straight or Reverse as long as staying on its work line primary reverse straight Technology and Reenginerring Term of energy, vector, resultante dan energy moment Energy has a direction to the left, right, upper side, under etc. Energy is a vector that is range that has direction. Technology and Reenginerring Term of energy, vector, resultante dan energy moment We can’t see energy but sense it. So, To describe energy in finishing building static problem, we need symbols. Symbol is scaling and direction line called Vector. Technology and Reenginerring Term of energy, vector, resultante dan energy moment For instance energy (P) = 100 kgs Energy scale 1 cm = 20 kgs so, vector length = 100 5 cms 20 Energy scale 1 cm = 20 kgs shows that 1 cm works for 20 kgs energy. Technology and Reenginerring Term of energy, vector, resultante dan energy moment TO FINISH BUILDING STATIC PROBLEMS BY USING PAINTING OR GRAPHICS Technology and Reenginerring Term of energy, vector, resultante dan energy moment Organizing or adjoining energy or if two energies or more could be linked to be a resulting one called RESULTANTE. Technology and Reenginerring Term of energy, vector, resultante dan energy moment Resultante symbolized R See this picture: Having combined to R, It has a different height and direction. P1 = Energy 1 P2 = ENERGY 2 R = Resultante Technology and Reenginerring Term of energy, vector, resultante dan energy moment Moment is a situation in which action and reaction is not in the same work line. Energy moment is the Moment multiplied by Length. M=Pxl M = Moment P = Energy L = Length Technology and Reenginerring Term of energy, vector, resultante dan energy moment Rules of moment : 1. If it rolls as straight as clock pointer, it’s called positive moment (+). 2. If it rolls inconventional, it’s called negative moment (-). SEE THIS PICTURES : Technology and Reenginerring Setting and dividing energy graphically and analitically Arranging or adjoining energy is to determine resultante (R), it means two or more energies can be joined to be one called resultante (R). Technology and Reenginerring Setting and dividing energy graphically and analitically Achieved by two ways Image method Calculation method Technology and Reenginerring Setting and dividing energy graphically and analitically This method must involve energy scales and draw it properly. An error in imaging will effect the result. Technology and Reenginerring Setting and dividing energy graphically and analitically Is on the same straightly work line Example: Set energy P1 = 50 kgs and P2 = 80 kgs on one track To be resultante (R). Conclussion : Decide energy scale for instance 1cm = 20 kgs a. Vector image P1 b. Relate vector P2 from the bottom side of P1 Technology and Reenginerring Setting and dividing energy graphically and analitically Work line P2 Work line P1 2,5 cm 4 cm R R = (2,5 + 4) cm x 20 = 130 kg (to the right side) Technology and Reenginerring Setting and dividing energy graphically and analitically Is on an inconventional work line example: Set two energies P1 = 150 kgs to the left and P2 = 50 kgs (to the right) to be a single resultante (R). Conclussions : Decide energy scale for instance1cm = 25 kgs Technology and Reenginerring Setting and dividing energy graphically and analitically Work line Work line P1 P2 50 25 2,5 cm 6 cm 4 cm Technology and Reenginerring Setting and dividing energy graphically and analitically 150 a. Illustrate vectur P1 = = 6 cm 25 b. Illustrate vector P1 = = 2 cm 50 25 So R = ( 6 – 2 ) cm x 25 = 100 kg ( left side ) Technology and Reenginerring Setting and dividing energy graphically and analitically Single work spot/ Different work line Different work spot Technology and Reenginerring Setting and dividing energy graphically and analitically Arranging energy with Paralelogram Arranging energy with paralelogram is so easy to do, but for one that is different direction and spot, may cause a complicated image. Technology and Reenginerring Setting and dividing energy graphically and analitically Example: Decide energy resultante of P1 = 100 kg P2 = 100 kg P3 = 125 kg With angles above Technology and Reenginerring Setting and dividing energy graphically and analitically Conclussion : 1. Decide energy scales for instance 1 cm = 25 kg. 2. Illustrate energy position with scaling. Make parallelogram with P1 and P2 as the side. 3. Pull the diagonal (made from P1 and P2 and R1) Technology and Reenginerring Setting and dividing energy graphically and analitically 5. Make a paralelogram with R1 and P3 as its side. 6. Pull diagonally from the angle R1 and P3 and to be R 7. Decide R length then multiplied with energy scale and that’s R Technology and Reenginerring Setting and dividing energy graphically and analitically See this picture : R = 10,2 cm x 25 = 280 kg If there are many energies, so the way used is the The same with above. Technology and Reenginerring Setting and dividing energy graphically and analitically Arranging energy with poligon Deciding resultante with poligon, we only connect one energy with the other, then the connector of the first work line with the last one, then we called it resultante (R). Otherwise, it move to the last energy. Technology and Reenginerring Setting and dividing energy graphically and analitically Example: Decide energy resultante P1, P2, P3 and P4 For instance energy scale1 cm = 30 kgs Solving steps : 1. Ilustrate the enrgy position with scaling. 2. Connect P2 from the bottom P1. 3. Connect P3 from the bottom P2. 4. Connect P4 from the bottom P3. 5. Connect the work line P1 to the bottom P4 that’s R. 6. Decide the length of R then multiplied with energy scale, that’s R total Technology and Reenginerring Setting and dividing energy graphically and analitically 1. Arrange energies scraching in single work line By inserting digit of energy where it must be positive if go to the right (+) and be negative (-) if go to the left or both. Technology and Reenginerring Setting and dividing energy graphically and analitically Case1 : R = 60 + 50 + 40 = 150 kgs (to the right) Case 2 : R = -120 + 40 + 30 = -50kgs (to the left) Technology and Reenginerring Setting and dividing energy graphically and analitically 2. Arranging two single work line energies but not in a single work line. The second Resultante of the energy P1 and P2 creating angle can be found with a formula : R P P2 2P P2 cos 1 1 Technology and Reenginerring Setting and dividing energy graphically and analitically Otherwise R position can be found with sinus formula P1 R sin sin (180 ) P1. sin(180 ) sin R Technology and Reenginerring Setting and dividing energy graphically and analitically Decide the resultante P1 and P2 that create 45 degree angle, also angle formed R Conclussion …. Technology and Reenginerring Setting and dividing energy graphically and analitically Conclussion : R P P2 2 P P2 cos 2 2 1 1 502 702 2.50.70 cos 45o 2500 4900 7000.0,707 7400 4949 12349 111kg Technology and Reenginerring Setting and dividing energy graphically and analitically P . sin(180 ) sin 1 R 50. sin 45o 111 35,35 111 0,3184 a sin 0,3184 18,57 o Technology and Reenginerring Calculating Energy moment If we wish to know moment, check this experiment Technology and Reenginerring Calculating Energy moment The three images are pieces of wood connected to Angle. Then, we hold from the vertical and we give Slight load (P) from upper side Technology and Reenginerring Calculating Energy moment , so it sense slight by our hands. We move the slight load (P) a litle bit to the right on the horizantal (image 2) so it will sense heavier otherwise the load is still the same. Then, we move untill the bottom horizontal wood then our hands are to weak to hold this load other wise this load is still slight. Technology and Reenginerring Calculating Energy moment From the experiment above, we can coclude on the first situation the load sense slight bacause the load scraches on the line with the reaction (there’s no moment) In the second experiment, the load sense heavier because it no more in the same work line with reaction (the moment is works). Technology and Reenginerring Calculating Energy moment In the third experiment, our hand are too weak to hold because the distance of action and reaction work line getting bigger (the moment get higher) So …… next slide Technology and Reenginerring Calculating Energy moment SO : 1. Moment is an event where an action and reaction isn’t in the single work line. 2. The total of moment is energy multiplied by distance 3. Unit of moment is unit of energy multiplied by unit of distance (kg.cm, kg.m, ton.cm, ton.m) Technology and Reenginerring Calculating Energy moment Case1 : A cube clipped vertically on a wall. The bottom of the cube is loaded P = 100 kgs. How big the moment in A? Conclussion … Technology and Reenginerring Calculating Energy moment Conclussion : A P = 100 kg L=2m Moment on A is : MA = P.L = 100.2 = 200 kg.m Technology and Reenginerring Calculating Energy moment Case 2 : Known : P1 = 150 kg A P1 P2 = 50 kg P2 Searched MA ? Coclussion : L=2m L=2m MA = P1.2 – P2.4 = 150.2 - 50.4 = 300 – 200 = 100 kgm Technology and Reenginerring M Calculating Energy moment Case 3 : A P1 P2 P3 L=2m L=2m L=2m Known : P1 = 100 kg, P2 = 40 kg dan P3 = 80 kg Searched : MA ? Conclussion : MA = -P1.2 + P2.4 - P3.6 = -100.2 + 40.4 – 80.6 = -200 + 160 – 480 = -520 kgm Technology and Reenginerring Calculating Energy moment Case 4 Contoh 4 : Psin 60 P = 1000 kg A Coclussion: 1. Describe P to vertical L=3m 2. Description Psin60o Known: P = 1000 kg MA = Psin 60 x 3 angle60o = 1000.0,866.3 Serched: MA? = 2598 kgm Technology and Reenginerring Describing kinds of loads on building static constraction calculation Technology and Reenginerring Describing kinds of loads on building static constraction calculation Decease Load Life load Wind Load Tremor Load Technology and Reenginerring Describing kinds of loads on building static constraction calculation Centered Load is not Edge Load divide well Load Technology and Reenginerring Describing kinds of loads on building static constraction calculation Direct Indirect Load Load Technology and Reenginerring Describing kinds of loads on building static constraction calculation Loads on building contructios based on its nature are : 1. Decease Load is all kinds of load comes from weight of building begin from the pondation to the roof 2. Life Load is all kinds of load temporarily load loading the building itself or its element. Technology and Reenginerring Describing kinds of loads on building static constraction calculation 3. Wind Load is all kinds of load on the building caused by winds. 4. Tremor Load is all kinds of loadon building caused by a tremor/earthquake. Technology and Reenginerring Explaining mean and kinds of load on building static calculation Based on its shape, load of a buildig is divide in to two : • Centered Load Is a load that has a small volume Example: pressing to train monorail by the train wheel 2. Spreading Load is a load that has spreading volume. example : Floor plat, concrete beam, and a pressuere on cocrete beam wall. Technology and Reenginerring Explaining mean and kinds of load on building static calculation 3. Centered Load is a load where the volume is spreading but its load isn’t divide widenly. Example : Forcing water on bathtube wall or forcing water on a eater gate. Technology and Reenginerring Explaining mean and kinds of load on building static calculation Based on its working of load on construction, on that load is given two loads they are direct and indirect loads. Technology and Reenginerring Explaining mean and kinds of load on building static calculation P a Load (P) direct to cocrete (a) Technology and Reenginerring Explaining mean and kinds of load on building static calculation P 1/2P 1/2P a b b Load (P) direct to the concrete (a) otherwise indirect to the concrete (b). Technology and Reenginerring Explaining mean and kinds of load on building static calculation Labelling these loads contains : For centered load : → P = 1000 kg, P = 12 ton, etc. For spread load : → q = 400kg/m, q = 2ton/m, etc. For wind load : → q = 20kg/m2, q = 0,02 t/m2, etc. Technology and Reenginerring Work principal of energy action and reaction An object A takes pressing energy to the other one B, so object B takes the same pressing energy to A but it has different direction received by B. Pressing energy A on B is called action energy while B to A is called reaction energy. So, Newton rule III; Action energy = Reaction energy Technology and Reenginerring Work principal of energy action and reaction As an exampel, see this : An object A with weight G is placed on flat floor B: N=G Because the object A is in silent, so Floor B will create reaction energy with amount N kg to the abject A. A So, N = G kg where direction of LANTAI B energy N contradicted to C. Those is Floor G called Normal energy. Technology and Reenginerring Work principal of energy action and reaction If the object A is in the blunt flat side pulled by an energy P1, this is why moving energy W1 coming between object A and those blunt flat. Because, moving energy W1 as same sa with P1 but it has contradiction direction, so the resultant energy is nil, W1 = P1. N=G A W1 P1 LANTAI B Floor G Technology and Reenginerring Work principal of energy action and reaction If the object A is in a blunt flat floor pulled with P2 energy where P2>P1 so object A-when it moves to the right, in the same time power energy W reaches the biggest score (W max). D N A Wmaks P2 > P1 B G Technology and Reenginerring Work principal of energy action and reaction When the object A is going to move, the object is still staying. So, Wmax = P2 Resultant energy from w Max and normal energy (N) is D Wmaks tgn N tgn = f is called energy coeeficient angle is called angle energy Technology and Reenginerring Work principal of energy action and reaction If the energy P2 tobe higher to P3, otherwise Wmax has a constant score In addtion P3 is bigger than W Max so object A moving to the right with acceration : P3 Wmaks a m Note : a = acceleration m = Object Mass A Technology and Reenginerring Work principal of energy action and reaction Rules of magnetism energy a. Magnetism energy straightly proportionates to normal energy N. b. Amount of Magnetism energy defends on kinds both materials, on its immense. c. Amount of Magnetism energy doesn’t defend on the immense, except if the volume is small and its deformation relatively huge. Technology and Reenginerring Work principal of energy action and reaction d. Magnetism energy is impossibly bigger than the energy from the silent object. e. Static energy between tow objects is tangensial energy forcing up one object to another. e. Magnetism energy is reaction energy contradicted to action energy direction. Technology and Reenginerring Work principal of energy action and reaction If energy P doesn’t work on the wall between object and floor (see image). N=G G b a W A G Technology and Reenginerring Work principal of energy action and reaction N=G W P Z A G Energy P and Magnetism energy W causes kopel +P.a. This is called Rooling Kopel and is balance where it is set up by normal energy N and weight energy G –Nb (stability moment) Technology and Reenginerring Work principal of energy action and reaction So Pa – Nb=0 or momen = 0. then, spot side of normal energy N moves to B to the right with length b. if the object will then roll, so the spot side N right to di A. Generally in energy term, if the object considered as material spot, alll kinds action and reaction energy is tyaken from spot side Z of the object Technology and Reenginerring Work Principal of EnergyBalances If the action and reaction energies are working on a work line concurrent, so the object is in balance with some rules : a. Amount of horizontal energy = 0 or H=0 b. Amount vertical energy = 0 or V=0 c. Amount moment=0 or MA=0, with A is a arbiterary spot on a flat land. Technology and Reenginerring Work Principal of EnergyBalances N=G W P Z A G From the diagram of action and reaction energy, we have a. P-W=0 b. N-G=0 c. Amount of energy momen to contradicted work line Z=0. Technology and Reenginerring Work Principal of EnergyBalances W N G P These are graphics calculation: Object is in balance if : a. Closed Poligon, resultan R=0. b. Energies through a single spot Z. Technology and Reenginerring Work Principal of EnergyBalances Notes : As a note that eventhough resultant R=0 that quite situaton not means balance, so we need to discover whether the object happend Technology and Reenginerring Work Principal of EnergyBalances See the image ! P The object isn’t balance R = 0. R=P- P r =0 Why isn’t it balance? P Because there is kopel on that object. Technology and Reenginerring Work Pricipal of momen kopel Kopel are two big, in line, and contradicted energies. Kopel is the same with moment where the amount kopel moment is the result of multiplying one of the energy with the distance of both energy. Technology and Reenginerring Work Pricipal of momen kopel P a P Momen Kopel = +P.a P a P Momen Kopel = -P.a Technology and Reenginerring Work Pricipal of momen kopel Nature of Kopel: 1. A kopel may be placed to the flat field where it comes ferom and on a flat field parraled to the place where the kopel is placed. see the image….. Technology and Reenginerring Work Pricipal of momen kopel B P MO1 = P.01B – P.O1A a = P(O1B – O1A) O 2 P = P.a →O1B – O1A = a A MO2 = P.O2B + P.O2A = P(O2B + O2A) = P.a →O2B + O2A = a O1 So, whenever spot O is taken kopen will not change Technology and Reenginerring Work Pricipal of momen kopel 2. A kopel has rotating nature on a flat field kopel. a P P M = P.a Technology and Reenginerring Work Pricipal of momen kopel screwdriver will be rotated by a kopel, so the moent kopel is M = P.a. Two kopels laying on a flat field may be added numerically Technology and Reenginerring Work Pricipal of momen kopel P1 P2 M1 = P1.a a b P2 M2 = P2.b MR = M1 + M 2 P1 If the kopel isn’t in single flat field otherwise on two flat fields. Technology and Reenginerring Work Pricipal of momen kopel V a P1 P1 P2 b P2 W MR = M 1 M 2 2M 1M 2 cos 2 2 MR Notes: M2 MR = momen resultante V M1 M1 = momen kopel P1 M2 = momen kopel P2 W Technology and Reenginerring Work Pricipal of momen kopel Two parrarel energies. Place resultante two parrarel energies can be counted with moment rules. A C B B C' P1 R P2 R = P 1 + P2 Technology and Reenginerring Work Pricipal of momen kopel R position is closer to bigger energy (P1) and stays on C. Based on momen rules : M R M1 + M 2 to spot A R.AC’ = O + P2.AB’ R = P1 + P2 (P1 + P2) – AC’ = P2 .AB’ AC’ = AC cos AB’ = AB cos Technology and Reenginerring Work Pricipal of momen kopel so (P1 + P2) AC cos = P2 AB cos (P1 + P2)AC = P2AB P1AC + P2AC = P2AB P1AC = P2AB – P2AC P1AC = P2BC → AB – AC = BC P1 : P2 = BC : AC conclussion………….. Technology and Reenginerring Work Pricipal of momen kopel coclussion : a. Amount of resultante (R) = amount of energy (P1 + P2) b. Direction resultante (R) takes one way P1 and P2 c. Resultante Position(R) between P1 and P2 and its work line (C) is closer to the bigger ones (P1). Position of work line C is decided by the comparison : P1 + P2 = BC : AC Technology and Reenginerring Work Pricipal of momen kopel Two parrarel and contradicted energy. position of resultante (R) two parrarel energies and contradicted can also be decided with moment formula : P2 C' C A B R = (P2 - P1) P1 Technology and Reenginerring Work Pricipal of momen kopel P1DP2 and P1P2 is also contradicted way. Direction of resultante is the same way with the biggest ones, in this term P1. Amount of resultante R = P1 – P2 Based on moment rules : MR = M1 + M2 (to A position) R : AC’ = 0 – P2.AB’ (P1 – P2).AC’ = -P2AB’ AC’ = AC.cos AB’ = AB. cos Technology and Reenginerring Work Pricipal of momen kopel -(P1 – P2)AC cos = -P2.AB cos (P1 – P2)AC cos = P2.AB cos (P1 – P2)AC = P2.AB P1.AC – P2AC = P2AB P1.AC = P2AB + P2AC P1.AC = P2(AB+AC) P1.AC = P2.BC AB + AC = BC P1 : P2 = BC : AC Technology and Reenginerring Work Pricipal of momen kopel Notes : a. Amont of resultante (R) = deviates of both energies (P1-P2). b. Position of resultante (R) is closer to the bigger ones (P1). c. Direction of resultante (R) is parrareled to the bigger energy. position of work line C is decided by the comparison P1 : P2 = BC : AC Technology and Reenginerring Improve your knowledge by yourself Thank you Compiled by : Deke Hernadin, S.Pd SMK Negeri 2 Kota Tasikmalaya Technology and Reenginerring