Concept explainers
Find the forces in the members of the truss.
Explanation of Solution
Given information:
Apply the sign conventions for calculating reactions, forces and moments using the three equations of equilibrium as shown below.
- For summation of forces along x-direction is equal to zero
- For summation of forces along y-direction is equal to zero
- For summation of moment about a point is equal to zero
Method of joints and section.
The negative value of force in any member indicates compression (C) and the positive value of force in any member indicates Tension (T).
Calculation:
Show the free body diagram of the truss as shown in Figure 1.
Refer Figure 1.
Consider the horizontal and vertical reactions at A are
Consider the vertical reaction at E is
Take the sum of the forces in the horizontal direction as zero.
Take the sum of the forces in the vertical direction as zero.
Take the sum of the moment about point A as zero.
Substitute
Calculate the value of the angle
Consider a section a-a passing through the members BC, CG, and JK.
Show the portion of the truss to the left of the section a-a as shown in Figure 2.
Refer Figure 2.
Take the sum of the moment about C as zero.
JOINT A.
Show the joint as shown in Figure 3.
Refer Figure 3.
For Equilibrium of forces,
JOINT J.
Show the joint as shown in Figure 4.
Refer Figure 4.
For Equilibrium of forces,
Substitute
JOINT F.
Show the joint as shown in Figure 5.
Refer Figure 5.
For Equilibrium of forces,
JOINT G.
Show the joint as shown in Figure 6.
Refer Figure 6.
For Equilibrium of forces,
JOINT E.
Show the joint as shown in Figure 7.
Refer Figure 7.
For Equilibrium of forces,
JOINT K.
Show the joint as shown in Figure 8.
Refer Figure 8.
For Equilibrium of forces,
Add Equation (3) and (4).
Subtract Equation (4) and (3).
JOINT I.
Show the joint as shown in Figure 9.
Refer Figure 9.
For Equilibrium of forces,
JOINT H.
Show the joint as shown in Figure 10.
Refer Figure 10.
For Equilibrium of forces,
Add Equation (5) and (6).
Subtract Equation (5) from Equation (6).
JOINT B.
Show the joint as shown in Figure 11.
Refer Figure 11.
For Equilibrium of forces,
JOINT D.
Show the joint as shown in Figure 12.
Refer Figure 12.
For Equilibrium of forces,
Show the forces in the members of the truss as shown in Table 1.
| Member | Force (k) |
| DC | |
| BC | |
| HD | |
| HC | |
| IH | |
| ID | |
| KH | |
| KI | |
| ED | |
| EI | |
| GB | |
| GC | |
| FG | |
| FB | |
| JF | |
| JG | |
| AB | |
| AF | |
| JK |
Want to see more full solutions like this?
Chapter 4 Solutions
STRUCTURAL ANALYSIS (LL)
- Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hzarrow_forwardA study of the ability of individuals to walk in a straight line reported the accompanying data on cadence (strides per second) for a sample of n = 20 randomly selected healthy men. 0.95 0.85 0.92 0.95 0.93 0.85 1.00 0.92 0.85 0.81 0.78 0.93 0.93 1.05 0.93 1.06 1.08 0.96 0.81 0.96 A normal probability plot gives substantial support to the assumption that the population distribution of cadence is approximately normal. A descriptive summary of the data from Minitab follows. Variable cadence Variable N Mean 20 cadence 0.9260 Min 0.7800 Median 0.9300 Max 1.0800 TrMean 0.9256 Q1 0.8500 StDev 0.0832 Q3 0.9600 SEMean 0.0186 (a) Calculate and interpret a 95% confidence interval for population mean cadence. (Round your answers to two decimal places.) strides per second Interpret this interval. ○ with 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval. With 95% confidence, the value of the true mean cadence of all such men falls above the…arrow_forwardWhat is the purchase quantity of 2 x 6 rafters needed for the roof and how many pieces of ridge shingles are needed for the roof? The slope of the roof is 4:12 and the exposure is 5 inches wide. arrow_forward
- For the system shown in Figure 2, u(t) and y(t) denote the absolute displacements of Building A and Building B, respectively. The two buildings are connected using a linear viscous damper with damping coefficient c. Due to construction activity, the floor mass of Building B was estimated that vibrates with harmonic displacement that is described by the following function: y(t) = yocos(2πft). Figure 2: Single-degree-of-freedom system in Problem 2. Please compute the following related to Building A: (a) Derive the equation of motion of the mass m. (20 points) (b) Find the expression of the amplitude of the steady-state displacement of the mass m. (10 pointsarrow_forwardThe direction of the force F_11 is __________LB. The magnitude of the force F_11 is __________LB.arrow_forwardIn the figure below, assume that complete mixing occurs between the two inflows before the mixture discharges from the pipe at C. Find: a. the mass flow rate in pipe C b. the velocity in pipe C Closed tank A c. the specific gravity of the mixture in pipe C Q=3 cfs SG=0.95 Diameter 6 in. Q = 1 cfs SG=0.85 B Diameter 4 in. Diameter 6 in. Q= 4 cfsarrow_forward
- MANUALLY DRAW THE FLOW NET. SHOW THE SCALE USED. do not just explain how to draw it, give me a completed flow net.arrow_forwardIn a simulation experiment on a single lane road, one vehicle is travelling at 18 m/s.After 1.5seconds, the vehicle suddenly accelerates at a rate of 1.5 m/s2 for the next2 seconds and remains0 acceleration then after. Simulate the behavior of subsequent vehicle with an initial speedof16 m/s using GM car following model for the first 3 seconds if the initial distanceheadwayis 20 m. Tabulate the results. Assume headway exponent 1.2, speed exponent1.5, sensitivitycoefficient 0.8, reaction time 0.6 seconds, and update interval of0.3 seconds.arrow_forwardFORWARD FROM POINT B TO POINT A GIVEN THE FOLLOWING: POINT BN=13,163,463.03'E=3,072,129.30' DIRECTION FROM B TO A (NAZ)=276.07529° DISTANCE FROM B TO A = 10.00'arrow_forward
- It proposed to provide pile foundation for a heavy column; the pile group consisting of 4 piles. placed at 2.0 m centre to centre, forming a square pattern. The under-ground soil is clay, having cu at surface as 60 kN/m², and at depth 10 m, as 100 kN/m². Compute the allowable column load on the pile cap with factor of safety of 3.0, if the piles are circular having diameters 0.5 m each and length as 10 m.arrow_forwardAt a particular section on a highway the following headways are observed: 0.04, 1.37,1.98,5.09, 3.00, 2.32, 2.54, 1.37, 0.94, 1.79, 1.10, 6.24, 4.82, 2.77, 4.82, 6.44. Fit an exponentialdistribution and compare the observed and estimated mean. Check the fit at the 5% level ofsignificance.arrow_forwardH.W: 1. Find the center of mass and the moment of inertia and radius of gyration about the y-axis of thin rectangular plate cut from the first quadrant by the lines x = 6 and y = 1 if (x, y) = x+y+1 2. Find the moment of inertia and radius of gyration about the coordinate axes of a thin rectangular plate of constant density & bounded by the lines x = 3 and y = 3 in the first quadrant.arrow_forward
