Problem 1 - Beam Analysis and Design Check
The idealised framing plan for an office floor system is shown in Figure 1. The floor will comprise of a 125mm thick reinforced concrete one-way slab, supported on steel beams with bolted end connections. The elevator shaft has 100mm thick reinforced concrete walls of 3.2m height, with door located above section EG. Your supervisor has asked you to perform a limit state (ultimate) analysis of Beam ST and check beam strength. Details are as follows.
Analyse Beam ST as follows:
1.1
a. Use shear and moment functions to derive the SFD and BMD for the ultimate load case. (Hint: Define FBD and calculate reactions first.)
b. Identify the maximum ultimate bending action in the beam, MMAX* and it's location.
c. Identify the maximum ultimate shear action in the beam, VMAX* and it's location.
1.2) Apply an additional concentrated live load of 10 kN at ‘F' on Beam ST.
a. FOR POINT LOAD ONLY: Use MOS to calculate maximum MPL* and draw BMD.
b. FOR ALL LOADS (PARTS 1.1 & 1.2): Use superposition to calculate ultimate bending action at ‘F', MF*.
Design checks for Beam ST:
1.3) Check actions from part 1.1 against capacity for the proposed beam, as shown in Table 1. Provide a concise summary of design recommendation for the beam, including FOS.
Input Data:
Dead Loads, G:
Reinforced concrete = 2450 kg/m3
Ignore self-weight of steel beams
Live Loads, Q (AS1170):
Office Floor, UDL = 3.0 kN/m2
Ultimate load case: LC1: 1.2G + 1.5Q
Ultimate Capacity of Beam ST
ØM = 174 kNm
ØV = 449 kN
NB:
FOS = Factor of safety > 1.0
= Ultimate Capacity/Ultimate Action
Problem 2 - Truss Analysis
The simply supported timber pedestrian bridge shown in Figure 2 crosses a creek in a local park. An equipment delivery to a substation requires a loaded vehicle to cross the bridge, and this load may be more critical than the normal pedestrian UDL for the bridge. The deck is comprised of simply supported sections which rest on joists. The deck and joists have been checked and satisfy capacity requirements for the new load, but an analysis is required to check the capacity of truss members. Ignore self-weight of the deck and the truss.
Determine the largest ultimate force in truss member FG, FFG* under vehicle loading.
Hint: Use Influence Lines and Trial and Error Method for moving load component.
Apply a 2.0 kPa live load over the entire deck instead of the vehicle load and determine FFG*. Which load is more critical for member FG?
Note: Deck width is 2.5 m.
Member design checks show that truss members are limited to the following capacity:
ØNT = 17.0 kN (tension)
ØNC = 8.5 kN (compression)
Provide a concise design recommendation summary for the truss, including FOS for critical load case.
Input Data:
Vehicle Live Loads, Q
Front Axle, QF = 0.5 T Rear Axle, QR = 1.35 T
Assume vehicle load is shared equally between the two trusses
Assume loaded vehicle moves right to left only (in direction shown in Figure 2)
Ultimate load case:
LC2: 1.5Q
