The forces in each member of the truss.
Answer to Problem 12.1P
The forces in each member of the truss are shown below.
The force in member AE is,
The force in member BF is,
The force in member EF is,
The force in member AB is,
The force in member CE is,
The force in member BD is,
The force in member DE is,
The force in member BC is,
The force in member AF is,
The force in member BE is,
The force in member CD is,
Explanation of Solution
Check the determinacy of the truss as shown below.
Here, number of members are
Substitute
Hence, the given truss is statically indeterminate by
The following diagram shows the free body diagram of the truss.
Figure-(1)
Write the equation for moment about A.
Here, vertical reaction at C is
Write the equation for sum of vertical forces.
Here, vertical reaction at A is
Substitute
Consider the force in diagonal members FB is in tension and AE is in compression.
Here, force in member AE and FB are
Use the method of section and cut the section as shown in figure below and calculate the forces in the members.
Figure-(2)
Calculate the angles as shown below.
Here, the angle between the members FA and FB is
Consider the joint F.
Write the Equation for sum of vertical forces.
Substitute
Write the equation for the sum of horizontal forces.
Here, force in member FE is
Substitute
Consider joint A.
Figure-(3)
Calculate the angles as shown below.
Write the equation for sum of vertical forces.
Substitute
Here, force in member FA is
Write the Equation for sum of horizontal forces.
Substitute
Here, force in member AB is
Consider the force in diagonal members BD is in tension and EC is in compression.
Here, force in member BD and EC are
Use the method of section method and cut the section as shown in figure below and calculate the forces in the members.
Figure-(4)
Calculate the angles as shown below.
Write the Equation for sum of vertical forces.
Substitute
Here, force in the member BD and CE are
Write the equation for moment about B.
Here, force in the member ED is
Substitute
Write the Equation for moment about E.
Here, force in the member BC is
Substitute
Write the Equation for sum of vertical forces.
Substitute
Here, force in the member BE is
Consider the joint C.
Angles will be same as calculated at joint B.
Figure-(5)
Write the Equation for sum of vertical forces.
Here, force in the member CD is
Substitute
Conclusion:
Therefore, the forces in each member of the truss are shown below.
The force in member AE is,
The force in member BF is,
The force in member EF is,
The force in member AB is,
The force in member CE is,
The force in member BD is,
The force in member DE is,
The force in member BC is,
The force in member AF is,
The force in member BE is,
The force in member CD is,
Want to see more full solutions like this?
Chapter 12 Solutions
STRUCTURAL ANAL.W/MOD MASTERING ACCE
- Please solve all pointsarrow_forward1: find out the optimal solution: 1- Reliability Function 2- Serial Configuration 3- M.T.T.F 4- Probability distribution function (P.D.F) 5- Failure rate function :calculate the reliability of the system for the following Figure 0.90 0.80 0.95 0.80 0.80 0.94) 0.80 : A system containing four connected compounds in series, each one has a distribution and its parameters as shown in the table below Component Scale parameter Shape parameter 1 100 1.20 2 150 0.87 3 510 - 1.80 4 720 1.00arrow_forwardTime: 1. Hrs During the last ten days: In one of the productive operations, the electronic control calculator equipped with No. of defects for a specific volume of samples as shown: 10 9 8 7 6 5 4 3 2 1 Day No. 6673 6976 7505 6991 7028 6960 7916 7010 6591 7350 Total No. 53 55 60 58 16 22 49 48 64 17 Defect No. DRAW THAT & CHOOSE THE BEST A-P chart. B-C chart 1. Key functions of quality control include: A) Control of design, materials received and products and conduct studies of operations B-Design and develop reasonable specifications C) The use of equipment that gives the required accuracy D) Provide appropriate screening equipment 2. The basic principles of critical pathways are: A-fragmentation of the system to the objectives of the secondary clear and specific B-Drawing the network diagram C-Finding the critical path D- All of the above 3- The production system is the following: A-An integral part of the plant's completion B-An effective system to integrate the efforts of various…arrow_forward
- ) We started a new production process and its study gave the total deviations The standard value (for 25 samples of the product, sample size 4) is .105 .Calculate the capacity of this process The product specification limits are: 6.30 = LSL 6.50 = USL Standard deviation in a manufacturing system is 0.038 = We made improvements to the system and the deviation has become Standard 0.030 = σ What is required is to calculate the estimated coefficient before and after the operation Optimization. What is your conclusion? : A find out the optimal solution: 1-Average Outgoing Quality AOQ 2- operating Characteristics Curve 100% Inspection 3-Acceptable Quality level 4- Average outgoing Quality AOQ 5- Capability Index CPKarrow_forwardFollowing are the data of gauge and discharge collected at a particular section of the river by stream gauging operation. Gauge reading Discharge Gauge reading Discharge (m) (cms) (m) (cms) 7.65 15 8.48 170 7.70 30 8.98 400 7.77 57 9.30 600 7.80 39 9.50 800 7.90 60 89 10.50 1500 7.91 100 11.10 2000 8.08 150 11.70 2400 1. Develop a rating curve for this stream at this section for use in estimating the discharge for a known gauge reading and fit a linear regression equation for use in estimation of stage for a known value of discharge. Use a value of 7.50 as the gauge reading corresponding to zero discharge. (20 pts) Equation 1 arith 2. What is the coefficient of correlation of the derived relationship? (10 pts) R2² arith Equation 2 log R2 log 3. Determine the stage for a discharge of 3500 cms (5 pts) 4. Determine the discharge for a stage of 15 m (5 pts) NB Do both arithmetic and logarithmic plotsarrow_forwardQ2/ A (2m x 4 m) rectangular flexible foundation is placed above the ground surface (G.S) for two layers of clay, each layer 10 m thick. The modulus of Elasticity (E.) of the upper layer is 13 MN/m² and that of the lower layer is 15 MN/m². The Poisson ratio is (u, = 0.6) for the two layers. The pressure (stress) of 100 kN/m²is distributed along the surface of foundation. Determine the rigid immediate settlement at the corner of the foundation using Elastic theory method?arrow_forward
- Q1/ Find the maximum allowable load for a square foundation (3 m x 3 m) placed vertically in cohesive soil? (Use Terzaghi equation) Note: Yt=Yeat=18 kN/m³ Depth of foundation = 1.5 m Depth of water table below the ground surface = 0.8 m Factor of safety 3 C=20 Yw = 10 kN/m³ = No vertical or inclined loadsarrow_forwardP.3.3 Oil of sp.gr. 0.9 flows through a vertical pipe (upwards). Two points A and B one above the other 40 cm apart in a pipe are connected by a U-tube carrying mercury. If the difference of pressure between A and B is 0.2 kg/cm², 1- Find the reading of the manometer. 2- If the oil flows through a horizontal pipe, find the reading in manometer for the same difference in pressure between A and B. Ans. 1- R= 0.12913 m, 2- R = 0.1575 m,arrow_forwardPlease solve the question by hand with a detailed explanation of the steps.arrow_forward
- Structural Analysis (10th Edition)Civil EngineeringISBN:9780134610672Author:Russell C. HibbelerPublisher:PEARSONPrinciples of Foundation Engineering (MindTap Cou...Civil EngineeringISBN:9781337705028Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage Learning
- Fundamentals of Structural AnalysisCivil EngineeringISBN:9780073398006Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel LanningPublisher:McGraw-Hill EducationTraffic and Highway EngineeringCivil EngineeringISBN:9781305156241Author:Garber, Nicholas J.Publisher:Cengage Learning