Concept explainers
Find the member end moments and reaction for the frames.

Answer to Problem 31P
The end moments at the member AC
Explanation of Solution
Calculation:
Consider the elastic modulus E of the frame is constant.
Show the free body diagram of the entire frame as in Figure 1.
Refer Figure 1,
Calculate the fixed end moment for AC.
Calculate the fixed end moment for CA.
Calculate the fixed end moment for CD.
Calculate the fixed end moment for DC.
Calculate the fixed end moment for DB.
Calculate the fixed end moment for BD.
Calculate the fixed end moment for CE.
Calculate the fixed end moment for EC.
Calculate the fixed end moment for EF.
Calculate the fixed end moment for FE.
Calculate the fixed end moment for FD.
Calculate the fixed end moment for DF.
Chord rotations:
Show the free body diagram of the chord rotation of the frame as in Figure 2.
Refer Figure 2,
Calculate the chord rotation of the frame AC and BD.
Calculate the chord rotation of the frame CE and DF.
Calculate the chord rotation of the frame CD and EF.
Calculate the slope deflection equation for the member AC.
Substitute 15 ft for L, 0 for
Calculate the slope deflection equation for the member CA.
Substitute 15 ft for L, 0 for
Calculate the slope deflection equation for the member CD.
Substitute 30 ft for L, 0 for
Calculate the slope deflection equation for the member DC.
Substitute 30 ft for L, 0 for
Calculate the slope deflection equation for the member DB.
Substitute 15 ft for L, 0 for
Calculate the slope deflection equation for the member BD.
Substitute 15 ft for L, 0 for
Calculate the slope deflection equation for the member CE.
Substitute 15 ft for L,
Calculate the slope deflection equation for the member EC.
Substitute 15 ft for L,
Calculate the slope deflection equation for the member EF.
Substitute 30 ft for L, 0 for
Calculate the slope deflection equation for the member FE.
Substitute 30 ft for L, 0 for
Calculate the slope deflection equation for the member FD.
Substitute 15 ft for L,
Calculate the slope deflection equation for the member DF.
Substitute 15 ft for L,
Write the equilibrium equation as below.
Substitute equation (2), equation (3), and equation (7) in above equation.
Write the equilibrium equation as below.
Substitute equation (4), equation (5) and equation (12) in above equation.
Write the equilibrium equation as below.
Substitute equation (8) and equation (9) in above equation.
Write the equilibrium equation as below.
Substitute equation (10) and equation (11) in above equation.
Show the free body diagram of the joint E and F due to sway force as in Figure 3.
Calculate the horizontal reaction at the member CE due to sway force by taking moment about point C.
Calculate the horizontal reaction at the member DF due to sway force by taking moment about point D.
Calculate the reaction of the support E and support F due to sway force by considering horizontal equilibrium.
Substitute equation (7), (8), (11) and (12).
Show the free body diagram of the joint C and D due to sway force as in Figure 4.
Calculate the horizontal reaction at the member AC due to sway force by taking moment about point A.
Calculate the horizontal reaction at the member BD due to sway force by taking moment about point B.
Calculate the reaction of the support C and support D due to sway force by considering horizontal equilibrium.
Substitute equation (1), equation (2), equation (5), and equation (6).
Solve the equation (13), equation (14), equation (15), equation (16), equation (17) and equation (18).
Calculate the moment about AC.
Substitute
Calculate the moment about CA.
Substitute
Calculate the moment about CD.
Substitute
Calculate the moment about DC.
Substitute
Calculate the moment about DB.
Substitute
Calculate the moment about BD.
Substitute
Calculate the moment about CE.
Substitute
Calculate the moment about EC.
Substitute
Calculate the moment about EF.
Substitute
Calculate the moment about FE.
Substitute
Calculate the moment about FD.
Substitute
Calculate the moment about DF.
Substitute
Show the section free body diagram of the member EF as in Figure 5.
Consider member EF:
Calculate the vertical reaction at the joint E by taking moment about point F.
Calculate the vertical reaction at joint F by resolving the horizontal equilibrium.
Show the section free body diagram of the member CD as in Figure 6.
Consider member CD:
Calculate the vertical reaction at the joint C by taking moment about point D.
Calculate the vertical reaction at joint D by resolving the horizontal equilibrium.
Show the section free body diagram of the member AC, CE, DB and FD as in Figure 7.
Calculate the reaction at joint A:
Calculate the reaction at joint B:
Consider member AC:
Calculate the horizontal reaction at the joint A by taking moment about point C.
Consider member BD:
Calculate the horizontal reaction at the joint B by taking moment about point D.
Show the reactions of the frame as in Figure 8.
Want to see more full solutions like this?
Chapter 15 Solutions
Structural Analysis, 5th Edition
- Problems 5-1 Stead flow of steam enters a condenser with an enthalpy of 2400 kJ/kg and a velocity of 366 m/sec. the condensate leaves the condenser with an enthalpy of 162kJ/sec and a velocity of 6 m/sec what is the heat transferred to the cooling water per kg steam condensed. (-69198 kJ/kg) 5-2 An air compressor delivers 4.5 kg of air per minute at a pressure of 7 bar and a specific volume of 0.17 m³ /kg. Ambient conditions are pressure 1bar and specific volume 0.86 m³/kg. The initial and final internal energy values for the air are 28 kJ/kg and 110 kJ/kg respectively. Heat rejected to the cooling jacket is 76kJ/kg of air pumped. Neglecting changes in kinetic and potential energies, what is the shaft power required driving the compressor? (14.3kW)arrow_forwardDetermine the design resistance to transverse force F,Rdarrow_forwardAs a structural engineer, your task is to design an optimum section that has sufficient resistance to the applied loading for the primary beam proposed in Figure 1. A UB in grade S275 steel is required for the unrestraint beam to carry the ultimate loads over the given span. Choose an optimumUB section and justify your selection. You are required to submit a design analysis by considering bending, shear, transverse force, and deflection checking for the selected member based on Eurocode 3 and the assumption of support condition and loading must be clearly stated. P=15 kN. a 2 m. b=3m ·L· ·b. Figure 1 Simply supported steel beamarrow_forward
- Why is it important to establish logical relationships between tasks when developing a construction schedule?arrow_forwardFor the gravity concrete dam shown in the figure, the following data are available: - Unit weight of concrete (Yeone) = 2.4 ton/m³ Neglect( Wave pressure, silt pressure, ice force and earth quake force) -0.65, (Ywater) 1 ton/m³ Find factor of safety against sliding and overturning (F.Said & F.Sover), If heel and toe stresses (Pais & Pmas) are 57.17ton/m2 and 84.53 ton/m² respectively. w.s.l 83m 10m 80m 8m Solve on paper step by step with sketcharrow_forwardWhy is proper planning important when developing a baseline construction project schedule?arrow_forward
- Determine the minimum possible surface area of a secondary clarifier treating activated sludge with a design influent flow rate (Q) of 1,000 m³/d, a return activated sludge (RAS) recycling ratio of 25%, and a mixed liquor total suspended solids (MLSS) concentration of 4,000 mg/L, if the overflow rate must be less than 33 m/d and the solids loading rate must be less than 250 kg/m²/d. Express your answer in m² and round up to the next integer.arrow_forwardEstimate the required air flow rate for the new activated sludge plant at Pea Ridge (Problems 23-223-723-10, and 23-13). The flow rate is 8,450 m³/day, the concentration of bCOD going into the system (So) is 137 mg/L, the concentration of bCOD leaving the system (S) is 16.3 mg/L, and the mass of cells produced per day (Pxvss) is 277.4 kg/d. Use the following assumptions to estimate the required air flow rate: . Clean water correction, a = 0.50 . Salinity correction, B = 0.95 Fouling factor = 0.9 Wastewater temperature = 12°C Atmospheric pressure = 101.325 kPa .Elevation 500 m . Depth of aerator = 5.6 m Operating DO 2.0 mg/L Percent oxygen leaving aeration tank - 19% ■ Manufacturer's SOTR = 535 kg/d Manufacturer's air flow rate at standard conditions 50 m³/d - aerator Express your answer with the units of m³/d and round to the nearest integer.arrow_forwardDetermine the required solids retention time (SRT) of a completely mixed activated sludge aeration tank for a conventional activated sludge system treating a design flow rate of 34,560 m³/d, where the effluent standards are 30.0 mg/L for BODs and 30.0 mg/L for total suspended solids (TSS). Assume that the BOD5 of the effluent TSS is 70% of the TSS concentration. Assume the BODs concentration leaving the primary clarifier is 128 mg/L that the MLVSS concentration (X₂) is 2,500 mg/L. Assume the following values for the growth constants: Ks 100 mg/L BODS ⚫ Hm - 2.5 d 1 kd = 0.050 d 1 Y = 0.50 mg VSS/mg BODs removed Express your answer in days and round to the nearest 0.1.arrow_forward
- Q1: Figure below shows loaded beam with its cross-section area, (A) Draw shear force and bending moment diagrams, stating the main values, (B) Find central slope and deflection, (C) Sketch the distribution of shear stress at left support, (D) Find maximum tensile and compressive bending stresses set up in beam at right support. E-205GN/m² P1 P2 P3 W1 W2 Lin Lin # A Length in (m) and loads in kN 3a a 2a 2a (Cross-section area, All dimensions in (mm))arrow_forwardEstimate the mass of oxygen to be supplied for a new activated sludge plant at Pea Ridge to treat a flow rate of 8,450 m³/day. Assume that the concentration of bCOD going into the system (So) is 137 mg/L, that the bCOD leaving the system (S) is 16.3 mg/L, and that the mass of cells produced per day (Pxvss) is 277.4 kg/d. Express your answer in kg/day and round to the nearest integer.arrow_forward*10-4. Determine the internal moments at the supports A, B, and C, then draw the moment diagram. Assume A is pinned, and B and C are rollers. El is constant. 3 k/ft 8 ft- 8 ft -4 ft-arrow_forward
